Maybe first read about the FFE and the DRJSCS in the article above this one.
You cannot work as a paid instructor in France without the appropriate qualifications.
Nothing under the BHSII will be recognised in France.
With the BHSII (or above) you can apply to your regional DRJSCS and you will have a form to fill in. Then they will want to meet with you to check you have an appropriate level of French to teach.
It will be a fairly informal conversation, to see your level of oral French, to check you can actually communicate fairly competently in French. (Or it was for me; as I am French it took no time; but I know an English instructor who passed it too).
Then they send your file to Paris where a national body meets 3 times a year, and discuss each file. Then you receive an official letter from the DRJSCS stating that they grant you an equivalent to :
the BPJEPS équitation (for BHSII).
or to DESJEPS équitation (for BHSI).
If you are NOT from UK consult IGEQ (The International Group for Equestrian Qualifications) on www.igeq.org
The following page of their website will show you the equivalence between each country: http://igeq.org/riding-instructor-eligible-qualifications.html.