Yes — EuropeanStack lists 4 European alternatives to Telegram, including Element, Olvid, and Threema. Each one has a verified European headquarters.
Element (United Kingdom) is the highest-rated European alternative to Telegram in our reviews, with an overall rating of 7.4/10.
Every alternative listed on this page has a verified European headquarters. 2 of the 4 are headquartered in the EU/EEA, where GDPR applies directly. All 4 also offer EU data hosting.