My initial thoughts are that perhaps you should get back into teaching in the UK for at least a year or two before relocating overseas.
What about the other parent? Is he/she amenable to you taking your child overseas to live? If the answer is 'no' then your dream is a non-starter.
I've had a few overseas postings, but my children only went to International schools in SE Asia; these schools pretty much 'pick and choose' which teachers to employ as so many teachers want to work overseas for a few years; they especially like 'trailing spouses' where the other partner is on an expat posting and the company is paying the rent.....so the school doesn't have to.
Otherwise international schools also like to employ husband and wife couples who are both teaching at the school....they only need to pay one housing allowance for the couple, rather than on an individual basis. In general, teachers at international schools have free (or greatly reduced) school fees at the school where they are employed for their children.
However - if you are an outstanding candidate then they may consider interviewing you. AFAIK many of the international schools advertise in the TES, sometimes directly but more usually through an agency.
My spouse's company have a lot of expat employees' children at an international school in central Switzerland; the teachers are mainly from the UK, Canada and some from the US. SA and Down Under....but they all teach in the English language and local Swiss people teach in German.
I lived in Singapore where it has a German school, a French school and a Swiss school in addition to all the other international schools. I would imagine though that they prefer to employ teachers who have recent experience teaching in those countries?
Switzerland is very expensive to live in and it will cost a fortune for childcare; I am unsure of the regulations for a foreigner to employ an au-pair who is supposedly learning the local language, but you would need an extra bedroom which will cost a lot more in rent. France will be cheaper.
I do have to say that it's popular for expats to be in countries where household help (eg. An amah/live in maid who helps with childcare and housekeeping) is not so expensive as in Europe eg. SE Asia, the Middle East and perhaps Cyprus which attracts domestic workers from the Philippines.
Good Luck!