Foley, 42, died overnight at the hotel, where the team were staying prior to Sunday's game against Racing 92.
The European Champions Cup game was postponed following the former Ireland international's death.
A statement by the Irish Rugby Football Union said: "The IRFU and Munster Rugby pass on our deepest sympathy to all of Anthony's family and friends."
It added: "We ask for privacy for the family at this sad time."
Foley is survived by his wife Olive and two children.