It was never really intended to be a viable nation, at least the aristocracy that led it never meant it to be. Its eventual collapse was caused by the fact that the Gallic Emperor (whose name escapes me right now) refused to take Rome when given the chance (when the Roman Emperor was away fighting against Zanobia in Palmyra), which cause Britain and I think Spain to return to the Roman fold.
If it were to live on, the effects would be interesting: a stable Gallic Empire would have been better capable of withstanding the Germanic invasions and surviving the collapse, Rome without the financial drain of Britain (although without the manpower of Gaul) might have survived longer as well, especially if later on the Gallic Empire and the Roman Empire remain friendly, at least in the interest of defense and preservation.