avoir le cœur sur la main

to be very generous

This expression describes someone who is extremely generous and giving.

Ma grand-mère a le cœur sur la main, elle aide tous ses voisins sans rien attendre en retour.

My grandmother is incredibly generous, she helps all her neighbors without expecting anything in return.

The image is of someone holding their heart in their open hand, ready to give it away. The poet Mathurin Régnier used it in his Satires in the early 17th century, and it was well established by the 18th. Unlike the English 'to wear one's heart on one's sleeve' (showing emotions openly), the French expression specifically emphasizes generosity.