I would think it would be at least somewhat plausible that, perhaps, a small colony of Archeops (or some other fossil species) managed to survive extinction and has been living for all this time in some remote location where few humans ever find them and therefore most people just assume they're extinct. After all, there are such things as "living fossils"; Relicanth, for example, is based off the coelacanth, a real life fish that's changed very little since prehistoric times and is still alive today. Horseshoe crabs, the basis of Kabuto, are also still around in the real world, even though in the Pokémon world Kabuto is apparently extinct. So for it to turn out that, in your Pokémon world, one or two fossil species aren't quite as extinct as you'd expect, it could just about make sense - provided you're careful with it. It's going to be a bit difficult to swallow that everyone believed Archeops to be an extinct species if there's a flock of them living just around the corner from Oreburgh, after all (and that's not even getting into the fact that its prehistoric habitat was in Unova, not Sinnoh).
Alternatively, like Dragonfree said, it might also be feasible that enough fossil Pokémon have been resurrected and released into the wild to start up a new population - perhaps some lab somewhere made a project of trying to repopulate suitable areas with once-extinct species and succeeded. If that's the case, you'll have to think about how well-known this is in your world: is it just a given to everyone that there's wild Archeops flying around now even though they were once extinct? Or is it something only really known to natural history geeks who are interested in the species in question and those who happen to live near the new habitat and got used to it, so that an unsuspecting passer-by would be surprised to see them there? And think about your main character in particular, too - is he one of those natural history geeks who would have found out about the Archeops Repopulation Project because he was interested? Is that maybe why he went there to try and catch himself a wild Archen?
Those are both possible ways of making it plausible that there'd be wild fossil Pokémon in your world; however, consider: does your world absolutely need to have wild fossil Pokémon in order for you to tell the story you want to tell? You say you're planning to have your main character attacked by a flock of wild Archeops - is it vital to the story that they're Archeops, in particular, or could you use some other not-normally-extinct species to fill in that role? As for your main character's Archen, I imagine it probably is important to the story that he starts with an Archen otherwise you wouldn't have chosen it, but why does he have to catch it from the wild? Is there any reason he can't just get it resurrected from a fossil? Fossil resurrection always struck me as potentially a rather neat way for a kid to get their first Pokémon, since it's one of the few ways to get hold of a Pokémon that doesn't require you to have a Pokémon already in order to battle and weaken a wild one. Maybe this kid likes Archen and Archeops enough that he specifically wanted to start with one, so his parents took him to Unova so he could dig up a Plume Fossil and then stopped by Oreburgh on the way back to get it revived. (And also, think about - even if it's important that the fic's set in Sinnoh, does your trainer necessarily have to start in Twinleaf like usual? He could always just start in Oreburgh as soon as he gets his Archen but spend a while training before challenging the Gym.)
I also don't understand the slight implication you seem to be giving that your trainer will only be able to form that story-important bond with his Archen if he caught it in the wild. If anything, your trainer should in theory bond even more easily with his Archen if he resurrected it from a fossil. Think about it: this hypothetical wild Archen is going to have had a whole separate set of experiences, memories, friends, probably its own parents if you view Archeops as taking care of their young, from its life in the wild. When suddenly it gets caught by a human boy and expected to become his friend and go on a journey with him, well, I'd imagine it'd take Archen a little while to get used to him and warm up to the idea. But if your trainer revived Archen from a fossil, then apart from possibly some faceless scientists in a lab (depending on how you interpret the resurrection process), that human kid is going to be literally the first thing Archen sees, the first person to talk to it, feed it, take care of it and generally be there for it. It's not going to know anything else; that boy will be its whole world. That's likely going to lead to Archen forming a deep bond with its trainer very quickly.
In summary: it's great that you want your story to be about fossil Pokémon. More fics should be about fossil Pokémon! But while there are ways to make it plausible that they're living wild, making them just like any normal wild species kind of slightly defeats the point of writing about fossil Pokémon. There's all sorts of interesting facets of fossil Pokémon that can be explored, from the unique way in which a Pokémon born in a lab is likely to bond with its trainer, to the implications of having species of Pokémon that any trainer who wants can obtain one to train but that died out in the wild millions of years ago and shouldn't even really exist in this world any more.
