The papers about his membership in the Légion d'honneur state his Christian names are Thomas-Pierre, and that he became chef de bataillon (it is a rank) on 22nd January 1815:

http://www2.culture.gouv.fr/LH/LH260/PG/FRDAFAN83_OL2471009V004.htm

This doesn't prove though that Thomas-Pierre Savarin of the 15e tirailleurs de la garde impériale is identical to the officer named Savarin who defended Saint-Denis.