You might be interested in this interview with Claude-Anne Lopez, who spent over 50 years as the editor of Yale's Papers of Benjamin Franklin and author of a number of Franklin essays. She downplays his supposed affairs basically putting much of it off as Franklin just being a big flirt. Although she does say "sex was quite plausible." And as she points out he did have one illegitimate child before he got married.

That sums up everything I've ever read on the man's affairs. At the very least he was an incorrigible flirt. And it is possible that he had affairs. If he did though, we have no direct hard evidence of them. He treated the subject with more openness and levity than was common at time. He even once wrote a piece advising a young man about how to select a mistress. It is impossible for me to imagine his contemporaries like Adams or Jefferson penning a similar letter. But that doesn't mean he had a mistress himself. As he often gave advice he didn't keep. And he had a keen wit. Whether true or not, I think the joke that Franklin wasn't allowed to write the Declaration of Independence because he might insert a hidden joke is insightful. It is hard to take anything he wrote as gospel truth.

So Franklin as a player? Apparently it remains plausible, but unproven.