can you use an arbitrary GPL'd FPS engine to implement Duke Nukem's gameplay on top of it? Yes you can
Well, one must be careful to choose a 3D engine that supports "sprites-as-models" for that though, otherwise there's a serious risk at ending with a more modern-looking game
As for FOSS game engines allowing to implement a 3D shooter... there's so much of those. So much of quake-derived engines, cube2, freedoom and the likes, descent engine can possibly be hacked into having some gravity...
I agree that the only thing required here is to create the content (I avoid the term asset on purpose, because content without code is useless), but it should not be considered easy. Otherwise someone would already have done it.
The graphical content itself (textures, sprites, rigged and animated models), you might find some random stuff at OGA, but: random. Can be placeholders until you can decide on an artistic line and redo all the work by yourself. Still, most of the stuff at OGA is not even rigged, so have fun. If I'm wrong, then please put a list of rigged models there (there are some, but really, few...).
Oh, to build humanoids models, there's the makehuman program. Can help to generate a good base, I think, but that's just a helper, the stuff it generates is way too detailed, and not rigged IIRC.
Then there's sound, music and... voice acting. This is likely even harder, but thankfully it's also less important to have something functional. I'd say decent voice acting is possibly the harder, this would certainly explain why almost no FOSS game I know have much of those (few games have some, but it's really some).
Last but not least, since that's one of the major parts of a game: maps and campaign.
By maps, I don't say textures or models or sprites used there: those can be placeholders, but the campaign scenario, the maps which punctuates it, with the progressive difficulty, their secret areas, their puzzles, their jokes (yes, many modern people don't like those jokes, but they're still jokes. Do you think the secret in 1st level when firing a big RPG rocket (even that weapon name feels like a joke) in the pr0n cinema screen, at *that* place is something serious?) and their place in the story.
This (about campaing and storytelling) is something which lacks in most FOSS games (outside of the RPG games). The only FOSS games which have actual stories (and lot of them, even) leading the player between maps that I know of is: wesnoth. Oh, right, Warzone2100 have one, too. But it started as non-FOSS game, people were paid to build it, because it was to be sold.
Widelands have few scenarios, but the stuff is mostly unfinished (at most 4 maps per campaign I think? And it's mostly tutorials, really). Platformer games like supertux and the likes just have an excuse, not really a story (each level don't really tell anything, sorry).
Oh, yes, there's openclonk too. But I still had to think more than few minutes to get those names.
I guess I could say weapons and inventory mechanics are also part of content, but I'm very unsure about that, since it's mostly code and balance.