The issue of whether to take exams early or not is interesting. I was debating this with someone recently regarding maths - she said nobody would say that an able musician should be held back because of their age, so why would you hold a mathematician back? DS, who's currently studying maths at Oxford, has also expressed that sort of idea - more so since being at uni with people from other countries with very competitive maths educations. The mathematicians talk about maths ability peaking in your 20s, so to maximise your own potential you might want to push beyond the usual timeframe. But this is specific to maths; with other subjects, what is the rush? Your ability does not have an expiry date. I think it depends if the child wants to have the opportunity to go to uni with people of their own age, and there aren't any easy answers. I certainly didn't want my child going to university early. And he wanted to study his favourite subject at uni, so if he'd pushed on ahead to Open University maths courses a few years earlier, he wouldn't then have had the same great experience that he has had now. You do have to think "To what end are they taking these exams early?" and ensure it fits in with their overall goals. If the goal is to become better at maths, sure, work at that - but that doesn't necessarily mean taking the exams early.
You can push a mathematician (or any subject specialist) in many ways other than just marching through the GCSE and A-level syllabuses as quickly as possible. Look for breadth and extension activities, rather than just more of the same. DS took his maths GCSE at 12 because he really wanted to, whilst home-educated. He then kept his maths current in other ways before going to sixth form to take his A-levels at the usual age. In the interim, he worked through A-level material, and the UK Maths Trust problems, plus other problem-based maths questions which were less linear than GCSE work, participated in the UKMT challenges, and read books about maths and biographies of mathematicians. These were all suggestions from someone involved in university maths admissions, btw.
If I had a child who was brilliant at French, rather than encourage her to take French A-level early, I would say - read in French, improve your French, but let's park up the exam until the regular time. We know you can ace the exam - let's work on your wider education. I would encourage her to take up other languages, to study language acquisition, the history of languages. There is so much that she could be doing to develop her talents and improve her education, other than rushing into her French A-level and kicking her heels for a few years until university.
I think this works for most subjects, doesn't it?