updated 03/17/2014 AT 2:00 PM ET
•originally published 03/17/2014 AT 2:30 PM ET
Klum, 40, looked chic and casual in a black peacoat and cowl neck, as Schnabel, 27, joined her in wearing sunglasses for their art walk in the City of Love.
The pair were spotted doing lots of smooching at an Oscar weekend party in Beverly Hills earlier this month.
Schnabel is the eldest son of director Julian Schnabel (The Diving Bell and the Butterfly), and he made a name for himself as a curator and art dealer while still a teenager. He dated Demi Moore in 2012, and has also been linked to Elle Macpherson and Liv Tyler.