It was quite a good game, but buggy as hell. Here are some facts I remember about it:

3D and FPP. It was a mix of FPS and RPG, set in the present (or the past, you could argue, as the game is from a bunch of years ago...)
There were dialogues with NPCs, trading, inventory management and that sort of stuff. As well as shooting, of course.
You played as an ex-military (French Legion, I think?), who travelled to some country in Central America in search of his missing daughter.
It was open world. There was a main town where the game started. Most of the map was composed of jungle. There were some other locations, like military camps, ruins, and small villages scattered around the country.
You could drive cars. However, there was a nasty bug that made your vehicle vanish from where you left it, along with whatever you had stored in its trunk, which could make you lose important equipment or leave you without any means of transportation in some remote part of the country.
The game featured day/night cycle and I'd swear it also had some destructible terrain.

I think the game could be the second part of another game, or had a second part. Not sure about this, tbh...
It also comes to my mind that the same devs that made this game also developed later a similar game in a sci-fi setting where you could travel with your ship to different planets. However, I think that project ended up being a badly unoptimized buggy mess...

Nothing to add from the immediate above, other than Boiling Point's prequel/second part was Xenus II.

Yes, that's Boiling Point!
Thanks a lot pals!
Now I'll look for its wishlist entry and vote for it :)

Yes, now there is a series that could do with a remaster! Played boiling point through years ago and enjoyed it, but tried more recently and couldn’t get back into it. The other two are very difficult to find. Possibly the far cry engine would be good for them, same sort of thing.

Xenus II and Precursors are on Steam, kinda surprisingly.