My DD1 y11 is doing both Spanish and French, so I might be biased.
I don't think the Ebacc as such is important, the school is measured on it but that should not be a reason for your son to do it if it's not in his best interests.
However, learning a foreign language is a useful skill. I think it is more useful in later life for him to do French than Music. If he can learn to 'have a go' in a foreign language he will be better equipped for later life, if only for holidays abroad.
Check the % of the CA. For DD she has 2 spoken and 2 written, each worth 15% (so 60% in total). Check also the format. DD's spoken are not a conversation. They prepare something in advance, learn it off pat, go in and spout it, and then get one unprepared question to answer. A diligent child can do well even with not much natural ability.
My view is that if he's never done formal grades in music he may well struggle with that too. It's not just playing a bit of something, there is a lot to GCSE music. French is more useful long term, even if only a basic GCSE standard. Presumably he's done 3 years of it already, so he should have a good grounding.
I think French GCSE 'looks' better than Music, but then I'm old and old-fashioned.
If he won't talk to the French teacher then he needs to stick with it.