The couple is out in the Hamptons right now, where they seem to have settled in to ring the 4th of July -- but before the fireworks, it looks like they were in the mood to get active ... namely, by hitting up a public pickleball court in Sag Harbor and whacking away.

Check out this footage, obtained by TMZ, which shows Bennifer hitting a ball back and forth out in the open. This was in a public space, BTW, so they weren't trying to lie low.

As you can see -- they're on the side of the court ... and we're told there were two children on the other end who were playing with them. No word on whether it was either of their kids or not, but ya gotta figure it might've been ... the brood rolls together a lot these days.

Now, when it comes to their game ... well, let's just say Jen looked to be a little more engaged (and dressed for the occasion) than her hubby did. She's out there in straight-up tennis gear (pickleball is like mini tennis, FWIW) and Ben's in ... jeans and a tee.

He also comes across as a little more lackadaisical here, half-heartedly using his paddle -- but hey, they're playing against young'ns. Can't really knock the dude for takin it easy.

Remember, the two of them had just gone to Michael Rubin's White party the day prior -- so it's possible they're a little pooped and soaking in the holiday with a chill back-and-forth.