i teach here in c.h and it was pretty easy for me to find a job- but i have graduate degrees in linguistics and tesol, along with years of teaching experience.
if you have degrees in early child care or teaching you may have luck in a private creche, playgroup or school, but experience and language alone won't get you a job. most employers want to see that you have pedagogical training and education. yes, in regards to charlie's comment, yes there are people here who speak english plus other languages so your best bet is to take some time and learn french- you can't expect your students to want to learn another language if you aren't doing the same
otherwise, in terms of babysitting- i know there are strict regulations on being registered with the canton to babysit- i would check out what you need and get that together as well as taking the time to learn french... it'll make your own transistion easier.