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...I totally understand why you might have adopted this poor bike, seeing it cast aside and unloved on a trash heap. I would only point out to you that from a purely economic standpoint, this is usually the most expensive way to acquire a commuter bicycle. There are plenty of likely candidates going begging, at very low prices, on most (if not all) local Craigslist and FAcebook marketplace lists, that already have all the parts on them, that will be easier to service than your old Peugeot, (because of its unique French standards for tubing diameters and threading). All of them will turn out cheaper and possibly better long term prospects for a commuter bike, and will be more easily maintained after you put them right.
What you are proposing as your project here is not impossible. It's just the single most confusing and expensive way to go about it, given your personal level of mechanical expertise at this point. I doubt anything I've said here will disabuse you of your idea, now that you have painted it. But I felt it needed to be said.
Best of luck.