No. Paul Bedard from the Animal Planet reality TV series Gator Boys is not married and has no children. There's no information published online stating that he is married or has children, and he hasn't mentioned having a wife or child on the show.
It's also uncertain whether or not he currently has a girlfriend or is dating anyone. His co-star, Jimmy Riffle, has mentioned in interviews that he has a girlfriend named Sara, who has also appeared on the show. It's likely that Bedard would have mentioned having a wife, child, or girlfriend in interviews as well.
Bedard is currently around 44 years old and has 20 years of experience wrangling and capturing alligators. He grew up in southeastern Massachusetts and has a degree from the University of Massachusetts. Before getting involved with rescuing alligators, he was a triathlete who competed at the highest level.
Gator Boys is now in the middle of its second season with new episodes airing every Sunday at 9 PM EST on Animal Planet. Due to their home base of Everglades Holiday Park in Fort Lauderdale, Florida being renovated, the Gator Boys have gone to Mississippi for most of Season 2, where their main task will be helping to capture alligators that escaped during Hurricane Katrina.