This is the correct ICAO procedure. The first wreckage was found in French territory so the entire investigation is now in their jurisdiction [1]. They are now leading the entire investigation. They are lumbered whether they like it or not with a long, tedious and expensive investigation.
In a complex case like this many nations will cooperate but in the end the final report will be published by the French.
Does that then mean the French should now take responsibility for the cost and recovery operations off our coast?