Planning a move to Lyon..much advice needed!

I am Greek, husband is French, we have been in England for over 15 years and we have two children under 4, we are looking to "temporarily" leave England and live in France for a year to see if we like it...not sure how Brexit influences this whole travel plan we have going on....just to clarify I am a translator working online (spanish, french, greek to english) and I intend to possibly teach privately if possible whilst in Lyon and my husband works offshore so we are not looking for local jobs. So here are some of my questions but ANY advice, information, pointers would be much appreciated in terms of what we should consider for planning our move.

1. BUDGET...we currently have a mortgage of Protected content month and we live in a nice suburban family safe area in a 3 bedroom house with large garden in Leicester. What is realistic to pay on a monthly rental somewhere practical and nice enough to enjoy family life in, near or even within 30 minutes drive from Lyon? We ideally did not want to spend more than Protected content a month on rent for a 3 bedroom apartment or house and we need to be close to amenities and schools. What do we like? like everyone, a mix of all worlds! Good access to the city, liveliness, safety, shops, markets and access to nice french schools (we can't afford private education)
2. SCHOOLING..how does the whole application system work for schools? We intend to visit Lyon as soon as we can in the New Year to visit some areas and schools and to get advice but I would appreciate at this stage some information on general information as to when you should apply for a place , which schools are nice for expats etc. I need to point out that my son understands english, french and greek very well but although fluent in english, he speaks basic sentences and has a general vocabulary for french and greek which we are constantly working on developing by trying to speak more french at home but still at this stage I am slightly worried for him in integrating at French school and enjoying the experience and playing with other children. He plays fine with other french children and his french cousins but is shy and can't construct sentences very well to explain himself as he would in english to say for example yesterday I played there tomorrow I am going there for example e.t.c. he will be 5 next year. On the other hand my daughter will be only 2 so I am mainly interested in her going to a nursery type setting whilst I work on a part time basis, how does this work in France, what are the costs and are there any that people can recommend?
3. THE MOVE...How is it done? Any advice, stories from experience are much appreciated. I am of course utilising common sense, organising and researching but I am interested in anything someone can share from their won experience.
4. SAFETY....My husband works away for weeks at a time so I really want to live somewhere where I can feel safe and independent with the children. Any suggestions?

I can't wait to hear from people in the know, I'm just so excited about this, can't wait to get the wheels in motion.