"Mary-Kate's family thinks Olivier is the best thing to happen to her," an insider told the magazine. "They love him."
Olsen, 27, and Sarkozy, 44, have been dating for about two years.
The UsMagazine.com report did not say when they got engaged or if they have set a wedding date.
Sarkozy is the half-brother of former French President Nicolas Sarkozy.
Olsen and her twin sister, Ashley, started out as child actresses alternating as the same character on the sitcom "Full House." They co-starred in a series of movies and now have a clothing and makeup empire.