What should I do with something I find that belongs to a non-Muslim and I cannot return it to him? And would I be sinful if I took it for myself?

Whoever finds money belonging to a non-combative disbeliever should treat it as a lost item (Luqatah). He should publicize it for a year through all possible means of identification. If its owner comes, he should give it to him. If the owner does not come, he may use it, and if the owner comes thereafter, he should give him its equivalent.