My question is: Is "La vie est belle" a specific idiom in French?
This sentence is a bit tricky. "La vie est belle" is a normal sentence in French but it's an idiom in an English-speaking context. Specifically, it's thrown around as a token French phrase when people want to humorously say something French but don't really know what to say. It's similar to the expression "voulez-vous coucher avec moi ce soir" which isn't particularly an idiom in French but will be used in an English-speaking context as a kind of "placeholder French", with a crasser effect in that case.
When a sentence like this one can be translated word by word in most if not all known languages without gaining or losing any substantial part of its meaning, you can't call it a specific idiom. It is at best a transparent one but then it would need an easily understandable figurative meaning too.
La vie est belle has a clear litteral meaning but not that much a figurative one, unless when used ironically.
I don't know if it is an actual idiom, but it is indeed quite common. The meaning is very close to the actual meaning of the words, so no surprise: it means you are enjoying your life. You may use it to make your friend know you're having good time :
— Ça va, tes vacances sur ton île paradisiaque ?
— Ça va, la vie est belle, je ne me plains pas...