At village level, the football teams are fun by the Village (Gemeinde/Commune) local football club - in conjunction with, but independent of the local school.
However, I am unsure how this would work in a city, such as Lausanne, which is centrally controlled, but sub-divided into districts.
EDIT:
Here is a list of Football Clubs from the Commune de Lausanne official website.
[link didn't reproduce correctly - in search boxes on r.h.s. select "Sport d'équipes" from first dropdown and "Football" from the second, then Rechercher]
Until, someone with direct experience, in your area, has a recommendation, they are a few links contained on this
search result page - which may or may not be of help.
I hope you can read the French - if not look for an option to translate (depending on your browser)