Upvote:6
You can enter Switzerland and stay there, for 90 days, under the usual rules which allow visa-free visits to the Schengen area for US citizens. The time spent in France under your French long-stay visa do not count towards these 90 days, see e.g. Does tourist visa (90 days) apply after a long-term visa ends in Schengen countries?
However I don't think you are allowed to do an internship in Switzerland without a Swiss visa/authorization (especially since I seem to recall that internships must be paid there), even during the validity period of your French visa.