Gillis was close enough related to this crowd to be considered an ancestor ~ Ann's the one who ends up in everybody's genealogy ~ and Gillis will be off on a jig on the Montmorency's a mere 20 years earlier. BTW, records generated in France from about 1380 to 1440 are not terribly reliable ~
De Rais only had one. His line is long extinct.
Anne Pot was born to Marie de Villiers, who was not the daughter of de Rais but of Guy de Nesle and Jeanne de Bruyere.
The records from France from 1380 to 1440 are as reliable as any from the period - what more accurate sources do you have than the available ones?
There is zero evidence that the Montmorencies descend from de Rais, which makes sense since that family can trace itself back to a knightly ancestor from 843.