Trierweiler sent Cassez books, chocolates and beauty products, and plans to send similar packages on a regular basis, her office said.
Cassez's case has caused diplomatic tension between France and Mexico since she was arrested and jailed in 2005.
Former French president Nicolas Sarkozy brought national attention to the case, irritating Mexican authorities who had hailed it as a successful arrest in a country plagued by kidnapping.
For his part, Hollande has called Cassez several times in prison and met with her parents at the Elysee palace.
Cassez, 37, maintains she is innocent and has launched an appeal.
In March 2012 the Mexican Supreme Court ruled against her immediate release, but said it would continue to review her case. A panel of five justices ruled 3-2 against releasing Cassez immediately, but four also said her rights had been violated.
Mexican president-elect Enrique Pena Nieto, who was elected in June but will be inaugurated December 1, is tentatively scheduled to visit France on October 17th. New administrations in the two countries could lead to new movement in the case.
Cassez and her ex-boyfriend Israel Vallarta were arrested in December 2005 in a "live" televised raid on a ranch to free three kidnap victims.
The raid actually took place hours after the suspects were detained elsewhere.
But the attorney general's office has stood by its prosecution of Cassez for organized crime, kidnapping and weapons possession.