PARIS—LVMH Moët Hennessy Louis Vuitton has agreed to buy Los Angeles-based eyewear maker Barton Perreira, part of the luxury conglomerate’s push to extend its reach to goods with mass-market appeal. 

Eyewear has emerged in recent years as one of the first purchases that aspiring luxury consumers make before moving on to more expensive items such as handbags. That is prompting LVMH and other luxury-goods companies to wean themselves off licensing agreements with third-party manufacturers and develop in-house eyewear operations.