@apsillers answer is correct, but let me say it in a slightly different way to convey the connotations.
"Far-fetched" means, as he says, unlikely to be true. Depending on context, it may mean that you think an idea is possible but unlikely, or it may be a polite way of saying that you think it is impossible or ridiculous. Like, scenario 1: "Maybe the president is pursuing this policy because he thinks the majority of the people are for it." "That's pretty far-fetched. Surely he's seen the polls." The theory is unlikely, but maybe the president hasn't seen the polls, or doesn't believe they are accurate. Scenario 2: "Maybe the president is pursuing this policy because he's secretly a Martian planted here to undermine this country as the first step in their invasion plans." "Well, that's ... pretty far-fetched." Your idea is absurd, but because you're my friend I don't want to say you're an idiot.
So yes, saying your friends proof is far-fetched is somewhere between meaningless and insulting. Generally we wouldn't say that a PROOF is far-fetched, only a theory or an idea can be far-fetched. A proof may be flawed, but a proof isn't a fact that can be true or false, it is an argument that can be convincing or unconvincing. I suppose you could say that a proof could be far-fetched in the sense of being unlikely to be VALID, though I think that would be an odd use of the word. But if you did take it that way, then you'd be saying that your friend's proof is extremely unlikely to be valid, i.e. it's a dumb idea.
"Far afield" means far from the center of things or far from where you started. In the literal sense, you could say "I travelled far afield", meaning, "I travelled far from home" or maybe "far from civilization". More often it's used metaphorically, like, "Dr Jones started out doing conventional physics research, but then he wandered far afield into theories about time travel and parallel worlds." Maybe I should clarify that it doesn't have to be that extreme.
I would be unlikely to say that a proof was "far afield", unless maybe it relied on very obscure information. Like if you tried to prove that a theory about current economics is true by using examples from ancient Babylon, I might say, "Wow, you're going pretty far afield to get evidence to back up your theory."
If I was trying to describe the situation you discuss, I think I'd just say, "Well, that proof is more complicated than necessary ..." If you want a single word, yes, "roundabout" would express the idea fairly well.