On another subscription site there is an entry in the Bulletin des Lois - I suppose the London Gazette would be a rough equivalent - stating that Capt. Th-M BESSON ceased active army service on 31 January 1863, married on 17 April 1856 (as you know), died on 12 January 1890 and was in receipt of an army pension, so 1,100 francs pension would be paid to his widow Fr-L PETCH, born on 2 January 1834 in Calais, living in Lyon, from 13 January 1890.
You say you don't know if Françoise-Louisa used the Besson surname. As you may know, a woman doesn't lose her maiden name on marriage in France so you would expect to find it on any official or legal documents.
Judith