I'll rent a car when I visit, but I'm curious about the parking situation near the beaches? Does one pay to park? Parking meters? First come first serve?

Parking meters? No offense intended but that’s funny. Most places you’re lucky if there’s pavement and/or lines.
Don’t over think it but the big DONT is don’t park if there’s a no-parking sign as you may well get your car towed away.

No offense taken, Pat.

Can you tell it's my first time!? haha

And for sure don't park on Pic Paradis, the highest mountain on the island--a great vantage point. Your wheels might disappear during your absence! Park long enough and maybe your engine will fly off, too, never to be seen again!

I don’t know this as fact and we always parked there when we used to go up to Pic de Paradis but we don’t go there any more.
I’ve heard a few locals say that as bad as petty theft here used to be, it’s gotten considerably worse of late. The comment made was, “lately, if it isn’t nailed down it’s apt to get stolen, and often even if it is nailed down it may still get stolen!”
Sad, but the world is changing all over.

We NEVER leave anything in the vehicle. We don't lock the car either. They don't have to break a window to find out there is nothing inside. We have had a side mirror stolen of of the car, though...

Car insurance is voided if you don't lock the vehicle! Sometimes they steal the car and not what is in it. You should rethink leaving the car unlocked.