That goes some way, but even 1835 seems far too late, and French influence is hardly going to go down better than German.
My intent was that the early monarchy had a role which was mostly symbolic, with cantonal liberty largely preserved. In essence, the early monarchy was basically limited to arbiting disputes between cantons, rather than setting policy for individual cantons. Frederick Augustus I himself was largely acted within those limits, and so wasn't seen as French influenced to start with. (The monarchy was imposed by
all foreign powers, so he wasn't seen as a French puppet initially.)
The problems started when the later monarchs tried to be more than just neutral arbiters of disputes... hence from 1835 on there was low-scale revolt at best and outright rebellion at worst.
The Helvetic Republic had collapsed within 3 years due to Napoleon attempting to reduce the Cantonal liberties, the Napoleonic Confederation was essentially the old Confederacy with a wee bit more central government. The King would probably have to be constantly moving between Cantons to prevent the development of a sense of favouring one canton, and he would be deeply, deeply unpopular.
He would certainly have to move between cantons regularly, and would not be all that popular at the best of times. Actively kicking him out, though, would probably wait until he actually started trying to rule.
Essentially, there's no real part of Switzerland that can give a support base for such a figure. He's too German for Neuchatel, Vaud, Valais, Ticino and the Bernese Jura, too protestant (and just generally a king and a foreigner) for the Waldstatten and Lucerne, and too Lutheran for the Protestants.
The kings of Saxony were actually Catholic, but ruled a Lutheran country. (Go figure, I know.) In that sense he was actually a good choice, because the history of Saxony showed that the Saxon monarchs, while they had a private faith, were scrupulous in respecting the recognised religious rights of other faiths. Catholics under the Saxon monarchs rule were not given special privileges; quite the opposite, they were excluded from rights.
Although I'd need to double-check to be sure, if memory serves Frederick Augustus was bilingual in French and German (a lot of German monarchs were), and so would be able to speak in French or German depending on which subjects he was dealing with.
At the very least, I would expect that we're looking at near constant low level rebellion and disorder for the entire period, and frequent open conflict.
I suppose low level disorder is entirely possible, but my main thoughts were that it would mostly start after 1835 because the later monarchs started trying to interpret their role as one involving actual power.