PARIS — I worked nights from a leather chair in my living room, armed with an iPad, a telephone and a notebook. My mission was to see if I could reconnect Jewish families and others with fine art pillaged from their relatives during World War II.

I have no degree in art history or particularly detailed knowledge of the Holocaust. My experience with genealogy is that of an amateur, one who traced my own family to 15th-century Spain.

But as a reporter, I track people for a living. And I was intrigued by the difficulties that French authorities report having as they try to find the heirs to more than 2,000 unclaimed works of art looted or sold under murky circumstances during the war and now held in French museums.

Over the past 60 years, the French have returned just 80 of the so-called orphaned works of art. The rest, some of them masterpieces, sit or hang in 57 French museums, which are their guardians until the rightful owners can be found....