I was intrigued by this question, because I wasn’t aware of any particular connection between the devil and fiddles (apart from Paganini’s story, already mentionned by a previous poster, but this isn’t exactly part of a traditionnal corpus of tales).
My take on the matter : generally speaking partying, dancing, etc… was considered rather sinful, and people enjoying it too much as putting their souls at risk. Thus, not surprisingly, the devil quite often tried to claim the souls of people who partaked too much in these activities, hence were already on the way to hell. For instance, the archetypal tale of the young woman seduced at a dance parlor by an attractive man who turns out to be the devil.
Musicians, and more generally entertainers were of course part of this crowd endangering their immortal soul. Not only were they directly involved in the local parties, but it was their main activity. They sort of encouraged others to take part in this frowned upon activity (that could also lead to other sinful behaviors, like drinking, having sex, etc…). They didn’t really “work” (as in : they weren’t breaking their back in the fields as a god-fearing christian should). Finally, they had an alternative lifestyle (in many tales, when something happens to a musician, it’s at night on the road when he comes back from the village where he performed. Good people shouldn’t be on the roads in the middle of the night). Finally, he had a peculiar and unusual talent, and a talent that influenced others (making them dance), that could easily be associated with magic.
As a result, musicians often appear in popular tales (for instance the common tale of the musician “hired” or rewarded by leprechauns or some similar creatures to entertain them while they dance). And so do musical instruments, often instruments with magical properties. Look at the famous piper of Hamelin, for instance.
So, why specifically the fiddle? At first, as I said, I was perplexed. Then I remembered a tale involving a fidle player and the devil (in this tale, the fiddle player can’t help playing his instrument while the devil drives him to a cliff and a certain death, until he manages, at the last moment, to invoke the Virgin Mary). And I remembered too an essentially identical tale involving a bagpipes player, from a region where, not surprisingly, bagpipes were a traditionnal instrument.
So, my guess is the following : there’s no particular and universal relationship between the devil and the fiddle. On the other hand, there’s commonly in tales a relationship between the devil, folk musicians and their instruments. And the instrument mentionned in such tales is whatever instrument that happens to be the most popular in the area where the story was told at the time when it used to be told (I would mention that folk tales, when they have not been “fossilized”, are generally adapted to the story teller’s public, by changing names, locations, animals, items involved, etc… to something familiar to the audience and that their last versions often date back to the 19th century). So, I suspect that this devil/fiddle association merely reflects the local popularity of the fiddle, probably 150 years ago or so.