The health and wellbeing of French acting star Alain Delon is in the spotlight in France amid a bitter family feud between his three living children over the veteran star’s medical regime and control of his assets.

Jean-Cédric Gaux, public prosecutor in the Loire Valley town of Montargis, close to the village of Douchy where Delon resides in a 19th century chateau, announced last week that he had appointed an authorized doctor to assess the health of the 88-year-old actor.

The move came amid a deepening succession dispute between Delon’s children, spanning eldest son Anthony, by French model Francine Canovas, and daughter and son Anouchka and Alain-Fabien, by Dutch model and TV presenter Rosalie van Breemen.

Gaux said he had taken the measure in response to two separate opposing letters from Delon’s lawyer Christophe Ayela and that of his son Anthony Delon, which both called for the...