Good to hear from you and I am sorry to hear your sad news. The Ainscough Tapestry sounds fascinating and no I have never heard of it before. Perhaps you could ask Michael for more information??
A French link is of course possible plus we need to remember that it is highly likely there were many Ainscough families probably with a range of origins too.
I shall do my best to find out more about this Tapestry - will blog your query when I get a moment.
take care and keep in touch.