It is reassuring to find that even the boss of a music streaming company can have his listening app commandeered by his children. Nestled among Alexis Lanternier’s top picks on Deezer is the Aladdin soundtrack, fighting for competition with Creedence Clearwater Revival and rapper Jul, the most listened-to artist in France. “My kids have their own accounts, but it can happen in the car,” says the father of four, who has run Deezer since September. The app is France’s answer to the big beasts of the streaming world: Spotify, Apple, Amazon and YouTube. Deezer is popular in its homeland but...