Hotels in Zürich are definitely expensive. Lots of business travelers, as well as tourist passing through.
Luzern (German spelling, which is what you will see in the area) is similar, in that case, because of the tourist demand. Often, less expensive than Zürich, but not by much. Interlaken as well has high tourist demand, although demand is tapering off in late September in the region.
My suggestion is to spend the first night either in Luzern,, or nearby, where cheaper accommodations can be found. After some time in and near Luzern, take the train to somewhere near Interlaken. Explore the Jungfrau area a bit, stay in one of the smaller villages, and after some more time on day 3, take the train or train and bus to Paris. I have not priced bus service, but train service from Interlaken to Paris is excellent, going through Bern.
Without having actually checked prices, towns north of Luzern along the train line are cheaper, as well as along the lake in places such as Merlischachen and other towns along that train line.
Check this sites pages for those major towns , and look under "hotels" as on this page which I have chosen for an example.:
Near Interlaken, you could look in Wilderswil, or, better for scenery, in the valley at Lauterbrunnen, Grindelwald or other towns.
At Luzern you get a beautiful old city, mountains and a beautiful lake.
Near Interlaken, outstanding alpine scenery.