1) I am not a lawyer. 2) My legal experience was in the U.S.A. not France or the U.K. I cannot and am not, giving you legal advice, but only my ruminations.
Complex.
2 countries. Different legal codes. I suspect, but only suspect that both countries have similar shared custody visitation schedules. Rotating annual holidays etc. That becomes less stable depending on the ages of the children and educational levels. It also depends on which country has home jurisdiction. English Law and Napoleonic code are different but both very western.
The children are likely to have a primary and custodial parent because you want to live in two different countries and I doubt the court or you and your husband will want to fly the children back and forth in a shared agreement. At 6 and 9 I doubt the court will either, but may have a different sharing plan than every other weekend and rotating holidays because of their age and distance.
If there is ANY dispute over who is the primary custodial parent, the court will have to look at the best interest of the CHILDREN. Or at least that is the standard in the U.S. 1)Who is the primary parent. 2) Which living situation is best for the children. 3) WHICH country has jurisdiction? 4) You may start with a French Lawyer but you ALSO may want to (I sure would) with a U.K. Lawyer as well.
They may ask: Who goes to parent teacher conferences? What are the names of your childrens teachers? When little Billy has flu and is vomiting, who stays up with him? Who takes little Jimmy to the doctor? Who takes little Osmeroid to school, dance class, etc. (this helps them figure out who the primary custodial parent is.
Probably a custody evaluation will have to be done by a professional. The issue of transporting children across borders is important as is the fact that they are U.K. citizens*.
His job is coming to an END.**
You say you are commuting, is your JOB*** in the U.K.?
How long have you been resident in France?
You OWN a home**** in the U.K.
Do you OWN one in France?
Finishing the year, where they are, has less impact on the children BUT you need to know if that affects their legal status in France. Dad might be smart on the issue on finishing the year for STABILITY for the kids. That's what 10 months? ( I don't have kids so have no clue when the school year is in France). If you can smile and be civil to one another the court will be happy, BUT ask the lawyer.
So, I'm not a lawyer, but I have sat through...God I don't even know...10 years of dissolution of marriage and child custody cases. I learned one thing...well a few things, but the one that stuck was, when people go through dissolution of marriage and child custody, they become deranged. Everyone. Not always in an obvious way (though I sure have seen that too) but inside you HURT. You have Anxiety, Anger, Fear, Loss and it makes BOTH of you less than ...optimal. Don't forget to take care of your emotional and mental self. See a marriage counselor or mental health therapist. The court may even order it.
I'm just throwing this out there, but the VAST majority of cases never go to court. If you can both think of the kids AND each other, it keeps you from savaging your kids and each other.
So those are things that you need to discuss with a COMPETENT Family law attorney...Barrister?
Things NOT to do.
1) Do not FIGHT in front of the children. It WILL come back to bite you and it will mess up your children. NO adult issues where they WILL hear (and believe me they do and they remember), the COURT and EVALUATORS will find out.
2) Do NOT transport them out of the country without your attorneys OK and the courts OK. If you do, it WILL come back to bite you. The court might REQUIRE you (or the children)to stay put until the issues are resolved.
3) Do NOT move to the U.K. and leave them with dad. Suck it up and stay in France, across the street if necessary UNTIL the custody and visitation issue is resolved.
4) Secure their passports but make them available WITHOUT delay if the court orders it...or it WILL come back to bite you. They may want you to turn the passports over to your Lawyer or the court.
5) What they want..."So do the children"...they are 6 and 9, I would be shocked if the court could care less what they want. That starts to change around 15 or 16 and the court MIGHT consider their opinion. Don't try to sway them. IF the court want's to know what the children want they will ask. Generally they DO NOT WANT the children within a Kilometer of the courtroom. Parents who insist on dragging their kids into court "to tell the judge what they want", are seen as not caring about the kids.
5) You NEED to be the parent who ALWAYS takes the high road in the interest of the children. The court and evaluators WILL know. You must always look like the concerned parent, calm and stable.
It's a process. It will take time and emotional energy and supreme calm. You have heard it, but it really is true: "You will no longer be wife and husband, but you will always be mommy and daddy."
Best of luck,