What’s it to be this morning? Brioche?” says Jacques Bellet, 86, to Bénédicte Picart, 18. They’re fixing breakfast, as they do every morning. They usually have dinner together, too. They live as roommates in Bellet’s apartment in Lyon, France.

Picart is one of approximately 1,100 students in France who take part in intergenerational home-sharing schemes. The group that organized her and Bellet’s home-sharing arrangement is ESDES Intergénérations, a nonprofit sponsored by the...

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