Hi, it's great to find a picture from so long ago. I wonder though if you've put it on the right family member. The picture is of Henri, Bishop of Puy , son of Charles Cauchon and Anne de Gondi. According to this site https://data.bnf.fr/fr/16224631/henri_cauchon_de_maupas_du_tour/ (it has another picture of him which might interest you), he was born in 1604. This would suggest that he was a couple of generations later than Thierry who died in 1554.