Martini was hospitalized after suffering cardiac arrest at the training center last week.
He has spent the majority of his career in Auxerre and Montpellier and has also played 31 times for France.
After a memorable 18-year career, Martini became goalkeeper coach with the France team which won Euro in 2000 and finished second in the World Cup in 2006.
“Today, French football mourns one of the greatest goalkeepers in its history and one of Montpellier’s most loyal servants, on and off the pitch,” the club said in a statement.
“He leaves the image of a good man, always ready to help, and who has never missed the opportunity to send a kind word to each of his interlocutors. Rest in peace Bruno, we already miss you. “
(Report by Rohith Nair in Bengaluru, edited by Pritha Sarkar)