The singer and "Emily in Paris" star hit the town Tuesday night in NYC -- following her surprise Times Square performance -- and they chowed down at celeb hot spot Carbone ... rocking matching all-black outfits as they came and went.

They also appeared to be getting into the same SUV ... and while there were no definitive signs of PDA -- the fact they were rolling together, in and of itself, kicked the rumor mill into overdrive ... namely, the notion they might be together as a couple.

The reason some might think that after seeing Shakira and Lucien together is because the dude is actually in one of her recent music videos -- for the song "Puntería" -- where he gets flirty and romantic with her on-camera. He was also in the mix for her Times Square gig.

So, seeing how he played her fictional BF ... many presume life is imitating art now -- and that they're, perhaps, hooking up. Like we said, there's no direct evidence that's the case.

Still ... we know Shakira is one of the most eligible bachelorettes in Hollywood right now -- so her getting with Lucien wouldn't really shock anyone ... he's hot, and she's hot, and they do look pretty damn good together.

Shakira has been unofficially linked to a few different dudes since splitting from her ex, Pique -- including Tom Cruise, Jimmy Butler and Lewis Hamilton ... but she never confirmed she was dating any of them, at least not officially.

Now, it would appear there might be a new suitor at her door ... that, or just a good pal.