The Cathedral is open every day for private prayer:

On the first Friday of the month, there is Eucharistic adoration after the 12:15 mass until the 5 PM mass. 

Every Thursday after the 5 PM mass, there is an hour of Eucharistic adoration in the chapel, with singing and prayers in French.
 
 

The Rosary is said in French, Monday to Friday at 4:20 PM (before the 5 PM mass).