Also, the description from the French coast guard of 'wreckage' rather than 'the aircraft' suggests the aircraft broke up on impact.
I'm afraid it did. Here is a link to a French Coastguard press release which contains a picture of a piece of wreckage.
Un avion de tourisme s'abīme en mer au large de Boulogne-sur-mer
I have also seen a picture of another fragment of wreckage which, sadly, identifies the aircraft involved conclusively but I don't want to post it here.