Just to address the "mountain fortress" bit, you should take a look at a topgraphical map of Switzerland. There are plenty of mountains but it's not like the country is surrounded by them. The big alps are to the south of some of Switzerland's biggest cities (Zurich, Bern, Basel) so an invader coming from the North could capture large chunks of the country's industry and population without going through the mountains.

You might be interested in reading about Switzerland's "national redoubt" strategy during WW2. The country's leadership knew perfectly well that they wouldn't be able to stop the Germans at the border if they invaded. Swiss strategy was for relatively small covering forces to delay the Germans while the bulk of the Army withdrew into the country's mountainous areas. A grim reality was that most of Switzerland's population would have been left behind in occupied areas that couldn't realistically be defended.

Hopefully someone else can provide a bit more detail on this last bit, but Switzerland in 1798 in no way resembled a modern nation state. The Old Swiss Confederacy was a very loose collection of mostly independent cantons with significant cultural, linguistic and religious differences. The French invasion succeeded because of political strife in Switzerland, not due to overwhelming military might.