The English word peripatetic means “tending to walk about; constantly travelling; itinerant; nomadic”. It is also related to Aristotle, his philosophy, and the school of thought he founded. A peripatetic teacher is one who teaches in a number of different schools, and it’s common, at least in the UK, for music teachers and sometimes language teachers, to be peripatetic.

It comes from the French péripatétique, from the Latin peripatēticus, from Ancient Greek περιπατητικός ‎(peripatētikós – given to walking around), from περιπατέω ‎(peripatéō – I walk around), from περί ‎(perí – around) and πατέω ‎(patéō – I walk). The French and Latin words mean “of or relating to Aristotle and his philosophy” [source].

The French for a peripatetic teacher is enseignant itinérant, and a travelling salesman is vendeur ambulant and a busker is musicien ambulant. The word péripatéticien(ne) does exist in French, but refers to a streetwalker / prostitute [source]. So should be handled with caution.