Back Market, Doctolib, Ornikar, HelloFresh, GitPod, N26, Yubikey, Revolut have plenty of impact and innovation as startups.
But maybe market cap is what impact means for you, so okay - Airbus? VW? Stellantis? Alstom? Thales? Safran? Sanofi? Siemens? Robert Bosch? Bayer? Literally among the best in the world in their respective branches. For instance, Airbus is outselling and outengineering and outinnovating and outmarketing and out-everything Boeing. Did you know that apart from them not being criminally negligent with basic safety systems, they're also heavily investing in all sorts of alternatives for the future of aviation? They have projects for battery-electric and hydrogen-powered airplanes, delta-wing designs, and collaborate with engine manufacturers (to be fair, it's a French-American Joint Venture) on innovative engine designs. Meanwhile Boeing's only innovation is NASA giving them a ton of money for them to test a new wing design for them.
Only some big names I could think of in France and Germany (and Spain and Netherlands and UK for Airbus). I really should start a list that I keep up for next time this topic comes up, people regularly underestimate innovation in the EU, or are completely unaware that said innovative company is European.