It is actually Swiss German that is the special case. The Swiss used to use Swiss Standard German (a very different beast with little difference to standard Standard German) about as much as Germans speak and spoke Standard German. But during the Second World War, for obvious reasons Standard German suddenly had very low prestige. The Swiss extended their dialect use enormously and even started writing in dialect. (This is still tricky even today, as there is no standard.)
Surely there was no such situation with standard French, and as a linguistic minority, French speakers in Switzerland have an incentive to identify to some extent with French culture.
Dialect leveling is of course a pretty universal phenomenon. I am sure it was accelerated by French policies, but I guess it's hard to say by how much. It certainly happens with German as well, with the notable exceptions of Swiss German and Luxembourgish, which are on the path towards full national languages for political reasons. I'm a native German speaker myself who never learned to speak a dialect.
As has always been the case, while languages and dialects disappear, new ones are formed and, initially ridiculed or marginalised. E.g. in Germany a new sociolect of urban youths is developing, in which a Turkish influence and special features of some German dialects are supporting each other.