Can the family court approve a settlement between parties if the agreement is just drawn up in English?

Yes, although the court may also request a translation or a parallel version in Hebrew, for reference, even if it only authorizes the agreement in English, which the parties sign.
This was the case in proceedings before Haifa Family Court in September 2016, where our law practice drafted a settlement agreement signed by the parents, and authorized at a hearing, bringing to an end custody,relocation and child support proceedings filed by the mother (our client) , and according to which the mother is relocating back to the U.S.A. with the minors.