I tested it. My mother always told me her maiden name (Bryant) was a Huguenot name, brought by French protestants escaping persecution. The site tells me it may be Breton. The name is distributed in Britain, even today like this. It is most common in Kent and Cornwall, which is consistent with a Breton-refugee origin. Page on the other hand was an East Anglian name in Victorian times by the look of it (I never knew that).
It's very interesting, but everyone seems to have cottoned on to this at the same time (as usual), so you may have to persist.
Other names in my family are Catholic (Rudge) Jewish (Jacobs) and Dutch (Gotch). I think we are all a mix of ethnicities as I have said before.
ETA - The International Huguenot Society records several documented 'ancestral Hugeunots' (I think from the 16th-18th Century) called Briant, so there may be something in my mum's claim.