I suggested to someone recently that the school choose Uncle Sam as the mascot.
Even if the school wants to stick to the F, you could slap some Fs where Sam normally has stars on his hat. I know, Uncle Sam wasn't really a senator, but he's a patriotic figure. I don't think there's really a general senator look, besides old white rich man in a suit. That's an ok mascot, I guess. Maybe bald and wearing a Navy hat.
When I searched for "senator Halloween costume," I got all Roman senator hits. That's not too bad, actually. US senators may be kind of boring, but a Roman senator is pretty sweet as a mascot. And you don't have to worry about being PC with the whole female senator thing because they didn't exist in Rome. Walmart even has a purple Roman senator costume for $26. I think I'll snap one up for my kids even if that doesn't become an official mascot.
I guess Fletcher could keep it simple and just use its namesake as the mascot, so instead of a generic senator, Duncan U would be THE senator himself, complete with heavy wool suit and handlebar moustache. He looks a little like the Monopoly guy. Actually, the only other team to be called the Senators that I know of was the Washington Senators (now Nationals--what's that?). I found two of their old-timey insignias, one showing a Monopoly-looking guy pitching (while smoking a cigar). The other depicted an outfielder catching a ball up against the Capitol, but the odd spotlight on him makes it look like he's about to be nabbed by the coppers (perhaps a January 6th rioter). Since Fletcher High School plays more than just baseball and it isn't even located in a state capital, using these wouldn't work.
While Duncan Fletcher was a senator, his wife was some kind of spiritualist, so Fletcher High School could take that angle with a witch or wizard mascot. Maybe both. And it would confuse the opposing teams, who'd be like, "I thought you were senators or beach rats. What's the meaning of this?"
Speaking of beach rats, I also like the idea of a dirty, disheveled rat. Like a homeless rat who lives on the beach and eats leftover french fries and washed up jellyfish. And who also could kick other mascots' butts in a bar fight (by cheating). Like Chuck E Cheese on meth, except wholesome (for the kids). So Chuck E Cheese on a Keto diet. Maybe with an eye patch.
When I first suggested a new mascot, someone in the house also thought of Fish. It's kind of general, but the alliteration works and you could change the species every few years if desired. Starkist has a giant Charlie the Tuna outfit, and I'm sure all kinds of Florida high schools have purchased plenty of other fish as mascots. Like Ponte Vedra High School. They have a dress-up shark as well as a real one that wanna-be-funny seniors hung from the rafters. (Side note: I told my kids that if I was in high school and played against the Sharks we'd all have called them Sharts along with lots of funny signs, images, and sound-effects. But I guess kids are more refined these days). The good part of being fish is you can have an early-season fish fry fundraiser. The school I taught at in Wisconsin always did a corn roast, though since the mascot was the Indians, it probably should have been a maize roast.
Sticking with the alliteration, Fletcher could be the Flamingos. I know, we don't have any Flamingos locally, but we also don't have any jaguars around here. Flycatchers and Fulmars are European birds that are pretty cool. Fulmars are like bad-ass seagulls that nest on cliffs and live to be 40 freakin years old. Since we're in Jacksonville and people love them some dogs, maybe French Bulldogs. I saw a house in Florida just got broken into and someone stole 20 French Bulldogs worth $100,000, so these are expensive dogs apparently bred in home breeding factories. French Bulldogs would allow Fletcher to have a mascot similar to Georgia, just smaller and cuter.
The main point here is that an F is not a team mascot. Students, alumni, boosters, and everyone at the Beaches ought to demand something better for the school. Since schools don't have newspapers anymore, I'm hoping this article can reach someone who cares just a little bit and can move the mascot /real insignia idea forward.