American Thomas Selldorff will reclaim six 18th-century paintings.
His Austrian grandfather sold them in 1941 to secure safe passage from France to Cuba.
A seventh work will be handed over to the family of Josef Weiner, a banker from Prague who died in the Nazi Holocaust.
In the hands of the Nazis, the paintings were destined for an art gallery that Adolf Hitler planned to build in his home town of Linz, Austria.
After the war they ended up in museum collections around France, where an estimated 2,000 are still pending identification.
Culture Minister Aurélie Filipetti said on Monday that France would cease waiting to be approached by the families and be more proactive in seeking out their rightful owners.
"A moral dut, a duty of the state," she tweeted on Tuesday afternoon.