Is the grave of Mary magdelin underneath a church in France?

Yes, Saint-Maximin-la-Sainte-Baume.The little town was transformed by the well-published discovery, 12 December 1279, in the crypt of Saint-Maximin, of a sarcophagus that was proclaimed to be the tomb of Mary Magdalene, signalled by miracles[1] and by the ensuing pilgrim-drawing cult of Mary Magdalene and Saint Maximin, that was assiduously cultivated by Charles II of Anjou, King of Naples. He founded the massive Gothic Basilique Ste. Marie-Madeleine in 1295; the basilica had the blessing of Boniface VIII, who placed it under the new teaching order of Dominicans.

The founding tradition held that relics of Mary Magdalene were preserved here, and not at Vézelay, (which also has a crypt that claims to have the relics) and that she, her brother Lazarus, and Maximin, a 3rd-century martyr who was now added to earlier lists of the Seventy Disciples, fled the Holy Land by a miraculous boat with neither rudder nor sail and landed at Saintes-Maries-de-la-Mer, in the Camargue near Arles. She then came to Marseille and converted the local people. Later in life, according to the founding legend, she retired to a cave in the Sainte-Baume mountains. She was buried in Saint-Maximin, which was not a place of pilgrimage in early times, though there is a Gallo-Roman crypt under the basilica. Sarcophagi are shown, of St Maximin, Ste. Marcelle, Ste. Suzanne and St. Sidoine (Sidonius) as well as the reliquary, which is said to hold the remains of Mary Magdalene.