You just cannot move a high school senior unless it's to an American curriculum international school and even then I wouldn't do it. (Brit in US FWIW, oldest in college.) If you must go for work, oldest is going to have to stay in America with a relative.
All the EU countries I know of (any exceptions I don't?) have school-leaving exams of some type that the students are preparing for 2-3 years prior. Even if you knew the local language you couldn't switch systems.
BFI (the replacement for OIB) is an extremely rigorous bilingual diploma, not one for newcomers. It's harder than the regular bac and you must still be fluent in regular French to pass it. French lycée pupils (2de - Tle or American 10-12th grade) go to school over 8 hours a day and then have piles of homework. There are newcomers classes but it would be intense work to reach the required standard.
The John F Kennedy School in Berlin is a free bilingual school, but again, you still need to know German and pass the Abitur exams.
Housing in NL is impossible right now, I have seen what friends have had to accept at extortionate prices after endless searching.
There really aren't free schools teaching entirely or primarily in foreign languages, especially not to a foreign curriculum. If your child were going into 11th grade then an IB school, rather than a national curriculum school, might fit better. But it wouldn't be all in English.