Onstage, the ex-senator and “S.N.L.” star doesn’t exactly address his fall from grace. But he doesn’t not address it either. Asked if he’ll run again, he is noncommittal.It was a fairly typical night at the Comedy Cellar’s Village Underground with a procession of young comics telling jokes about bickering couples, body issues and unglamorous sex. After Matteo Lane finished his set with a story about sleeping with a porn star, the curveball came: The host introduced “the only performer on the lineup who was a United States senator.”Then Al Franken, 70, bespectacled and wearing a button-down shirt, slowly walked onstage. He looked back toward Lane, took a considered pause and in mock outrage exclaimed: “He stole my act!”Franken has been opening with that joke a lot lately as he’s been refining material in basement rooms around town in preparation for a national stand-up tour. It’s his way of addressing how much he sticks out in his return to comedy, following a Senate career that ended with his resignation after multiple women accused him of sexual misconduct, including unwanted kissing. New York comics generally don’t do impressions of the Republican Senator Chuck Grassley, of Iowa, or earnestly explain the reasons they remain Democrats. And yet, the four times I have seen Franken perform over the past month, he has consistently gotten laughs or even killed. The only time he really lost a crowd was after midnight when the fury of a rant about the Republican Senator Ted Cruz, of Texas, (involving a dispute about an assault weapons ban) crowded out the punch lines. Franken’s set went long, around 50 minutes, and a couple of comics who followed needled him. “I would have killed myself if it wasn’t for his gun legislation,” Nimesh Patel joked.In Franken’s new material, he explains how as a politician, he was often implored by his staff to not be funny. It only leads to trouble. His act presents a less censored Franken, one that includes a story of him inside the Senate cloakroom telling a joke about oral sex with Willie Nelson — with Franken deftly imitating the New York Senator Chuck Schumer and former Missouri Senator Claire McCaskill, both Democrats, as they dissect the joke. Franken’s delivery is a Minnesota mosey with a bristling energy hinting at unspoken feelings and future ambition.On the street after the Cellar show, Franken and I discussed Norm Macdonald, who had died earlier that day. Franken mentioned that when he was on “Saturday Night Live,” Macdonald had beat him out for the Weekend Update anchor job, then recalled how the NBC executive Don Ohlmeyer supposedly fired Macdonald for making jokes about O.J. Simpson, Ohlmeyer’s friend. Franken quipped: “Got to give credit to Ohlmeyer for sticking by a friend.”It’s a funny joke, but as often happens with Franken these days, it can’t help but evoke his own scandal. After all, many of Franken’s colleagues did not stick by him in the wake of the accusations. After a photo of Franken pantomiming groping a conservative talk radio host on a U.S.O. tour was released, many Democratic senators called for him to step down, and he did, denying the allegations in a resignation speech. Since then, many (but not all) Democrats have seen that reaction as a rush to judgment, including nine senators who had called for him to resign now saying they regret doing so. Some politicians who stood by their calls for him to resign, like Senator Kirsten Gillibrand, Democrat of New York, have faced a backlash.Franken only recently began explicitly mentioning the fallout onstage, but glancingly, with a bit involving a masked ventriloquist’s dummy named Petey who wants to talk about how he was treated by his Democratic colleagues. Without giving away the twist, the conversation gets sidetracked.Is the comedy tour a way to rehabilitate his political career? Franken said, with a laugh, “I’m not sure this is the best way to do that.”Todd Heisler/The New York TimesAt an Upper West Side diner, Franken didn’t want to go into details, calling it a “no-win,” but said it hasn’t changed his politics. “Part of the irony of all this is I was maybe the most proactive member of the Senate on sexual harassment and sexual assault,” he said.As for his old co-workers: “I have forgiven the ones who have apologized to me,” he said, tersely.Outside the diner, a man approached and told him that he looked more handsome in person and then said in a pointed way that seemed beyond politics: “I’m in your camp.”At a few of the New York shows, there was a certain tension in the room before he got onstage, and a curiosity over how warmly he would be received. Franken said he was never anxious about it. “People like me,” he said, in a cadence that couldn’t help but evoke his character Stuart Smalley, the 12-step aficionado he portrayed on “Saturday Night Live.” After I pointed this out, Franken burst into an impression of the cheerfully cardiganed character: “I’m fun to be with.”Franken — who moves effortlessly from inside-showbiz yarns to political ones — is less deadpan offstage than on, with a slightly quicker delivery, puncturing many sentences with a booming laugh that sounds like a baritone quack.Long before he was a politician, Franken, who moved from Washington to New York in January to be near his grandchildren, was something of a comedy prodigy — performing at the Comedy Store in Los Angeles in a double act with Tom Davis while still in college, and going to work as a writer for the original cast of “Saturday Night Live.” He then pioneered a no-holds-barred style of liberal comedy with best-selling books like “Rush Limbaugh Is a Big Fat Idiot and Other Observations.” Franken still delights in skewering the right-wing media entertainment complex amid dissections of public policy, which he does regularly on a titular new podcast that welcomes a starry list of politicians, journalists and entertainers. In his show, he says, “The leading cause of death in this country is Tucker Carlson.”Franken says he is returning to comedy because it’s a “part of him,” and his conversation is filled with references to friends in the business. He said he went to the Cellar after speaking with Chris Rock and Louis C.K. But it’s hard to escape the impression that politics animate Franken more than comedy. He said he loved campaigning and being a senator, and for someone as well-known as he is, his act includes an awful lot of résumé highlights (like casting the deciding vote for the Affordable Care Act) coddled in a layer of irony that knows you can get laughs by playing the jerk. “You’re welcome” is a recurring punchline.His act presents a less-censored Franken. Todd Heisler/The New York TimesThere are moments onstage that have elements of a stump speech, and it makes you wonder if this is all a prelude to another run. When asked, Franken shifted from casual comic to preprogrammed politician: “I am keeping my options open.”What about running for senator of New York? He repeated, “I am keeping my options open.”After chuckling at this diplomatic answer, I pointed out I’m not used to interviewing politicians. Franken let out another quacking laugh and acted out a scene imagining the ridiculousness of a comic answering a question about a joke with “I am keeping my options open.”It’s worth noting that even in his telling, the first time Franken ran for senator in Minnesota, his original impulse involved a measure of payback. After Senator Paul Wellstone died in a plane crash, his successor, Norm Coleman, called himself a “99 percent improvement” over Wellstone. In his book “Al Franken, Giant of the Senate,” he describes his reaction with a flash of anger, saying he knew someone had to beat Coleman, before adding that his reasons expanded from that “petty place” to one more about helping the people of his state.In the aftermath of his scandal, which Franken described as “traumatic” for him and his family, he has been trying to work through it and rise above, he said. “I think we need more of that. It’s a struggle but I’m getting there. That’s my goal.”In a sympathetic New Yorker article from 2019, Franken said that after losing his job, he started taking medication for depression; mental health is an issue he has long worked on, he said. When I asked about this, the policy wonk, not the comedian, answered. He brought up the first legislation he passed, calling for a study of the impact on giving support dogs to veterans suffering from PTSD. The conversation moved to the gymnast Simone Biles and how she prioritized her mental health at the Olympics. Franken brought up the people who criticized her, appearing to earnestly address Biles’s situation before making a sarcastic pivot subtle enough that it took me a beat to appreciate the subtext. “So odd — people criticize other people out of ignorance,” he said, a hint of a smirk on his face. “I’d never seen that before. I was just shocked.”When asked what he would say to someone who thought this return to comedy was a way to rehabilitate his political career, Franken said: “I’m not sure this is the best way to do that.” He offered another big laugh before getting serious. “I’m doing this because I love doing this.”On Sunday, running his entire show at Union Hall in preparation for a Friday performance in Milwaukee (it’s not often you hear material in Brooklyn about the Republican Senator Ron Johnson), Franken earned a roaring response to his dummy nudging him to talk about leaving the Senate. At one point, a member of the audience yelled: “Run again!”As the crowd cheered, Franken looked momentarily flustered and flattered. He appeared to be contemplating his next move or maybe weighing a joke. But instead, he made eye contact with the man egging him on and said: “I will need your help.” More