Nice!
After acquiring the needed parts you should be into it for less than it's $250-350 value. It needs the stacking hook part of the upper barrel band as well, but hopefully that will be included with the barrel band (as it should). I don't think this version needs a floor plate as most (all?) 3-round versions never had one. This is a true M1907_15, not a M1907_15 modifie 1916, which took the five shot "chargeur" (en bloc clip). Mismatched parts is the rule rather than the exception with these French rifles since most were rebuilt many times during or after the carnage of WWI.
If it has the N on the barrel, then it'll take modern produced (PPU) ammo, which is based on the Modèle 1932N cartridge, if not you'll have to reload for it. I assume it is N marked based on your dismissal of the seller's story, and you'd be correct in dismissing it. That was a 1932, or shortly thereafter, modification. Many were imported before 1968 so no import mark is no guarantee that it was brought back from WWI. It seems very unlikely that a US vet would have been allowed to bring back a weapon used by one of the US allies.