French and Italian tolls are extremely expensive. We are used to paying in one day tolls in France that are more than our vignette for the whole year.

The only toll you might come across in Switzerland, going to Italy, depending on the route you take is the St Bernard tunnel. This is quite expensive. It is the only one in Switzerland that charges a toll. (reason - the northern entrance is in Switzerland but you cross into Italy in the tunnel and exit in Italy and the tunnel is operated by an international company.)

I would stay a night around Rheims. Enjoy some champagne! Then next night somewhere like Montreux . And then go on to Italy, going over the Simplon pass which will take you past Domodossola to Stres.

The fastest route according to Google maps is via Reims, Troyes, entering Switzerland near Vallorbe for Vevey, Martigny, Simplon mountain pass, some 1200 km in 14 hours. Viamichelin shows similar routes with in addition cost estimate with details such as road toll for an itinerary. A slightly longer, less toll roads is via Luxemburg, enter Switzerland in Basel for St.Gotthard route (mountain pass road still not open) to Locarno, then along Lago Maggiore west side to Stresa.

France toll road system is using toll booths, options to pay cash or card (less and less manned); an option is to get a transponder for using the fast, no-stop lanes (several offers for not frequent users; now available also for motorways in France, Spain, Portugal and Italy, webpage to start is for example https://www.telepeagelibert.com/ imho getting such a device makes sense if traveling at least every second year once on motorways in France or the other countries on the list.

For a summary on motorway vignette for Switzerland see for example https://www.tripadvisor.com/ShowTopic-g188045-i336-k14748964-Info_Switzerland_motorway_vignette-Switzerland.html#120644045

I have driven similar distances in a day (not recommended), for that route I would consider an overnight stay in Champagne region (or for example near Troyes "Parc naturel de la forêt d'Orient) or Alsace (one of the smaller villages).

When planning such trips now I try to adjust as far as possible to avoid expected major traffic jams, especially on vacation time. Basically avoid entering metropolitan areas during morning rush hours, leaving during afternoon rush hours. Avoid as far as possible weekends, definitely St.Gotthard route on any vacation Saturday. France has an official website on travel recommendation at https://www.bison-fute.gouv.fr/index,langen.html to avoid extremely busy travel days and routes. Check also for France environmental sticker "Crit'air", costs less than 4 Euro at government website https://www.certificat-air.gouv.fr/ and is already required for a few cities, will be in more regions in case of increased air pollution.