As PPs have said, Foundation is the same GCSE as Higher.
In my subject, English, Foundation covers grades from U up to B, whereas Higher covers grades D-A*.
we generally enter students for Higher if they have a fighting chance of a B. The final decision on which tier isn't taken until year 11 - & even then, I've currently got a lad in my top set who'll be doing Foundation if he can't show me a convincing C in his February Mock.
If the only concern you have is that your ds is being entered for Foundation tier GCSEs, that's really not a problem. No one will ever know which paper he took to gain his grade Cs. If he does blossom later he can be entered for Higher at any point up to the day he sits the exam.
what you do need to look out for is:
-limiting subject combinations (eg. separate Sciences are usually reserved for the more academic students, & not having them closes certain courses off at A Level & onwards),
- any qualifications that aren't GCSEs - you definitely need to establish in that case whether whatever they want to put him in for is going to be an equivalent qualification, which is recognised & accepted by FE/employers. Some BTECs & what have you are at least as rigorous, but different; others not so much.
As for whether you can insist - no, I'm afraid you can't. The school will make the ultimate decision as to which exams they're prepared to enter him for, based on their judgment as to which tier/qualification he's most likely to be successful at.
There's nothing to stop you entering him privately for exams the school aren't prepared to put him in for - except that if it's a question of the tier, both Higher & Foundation papers are sat simultaneously - so that's not terrifically practical. It might theoretically be feasible to enter him for a subject he isn't entered for at all, but then you'd need him to have been taught outside of school to the sort of level whereby he'd do well. Not really do-able in subjects with Controlled Assessment, either...
The simplest answer, tbh, is to convince the school that your ds is about to demonstrate the ability he has yet to show - & put a rocket under ds!