I think the EU would be very happy with every major company running their own FOSS stack instead of handing their money/control to US tech firms.
Sure, this doesn't mean the EU would have control over the FOSS stack, but it would keep the data/money/soft power away from the US. And the EU would have a much easier time enforcing its security/privacy laws on those EU companies running FOSS on hardware inside the EU.
Because the EU is relatively low-corruption so far EU goals trend towards transparency, privacy and interoperability (despite some efforts to the contrary). FLOSS naturally aligns with these goals, without needing extensive threats or control .
The EU doesn't control FOSS any more than it does US tech, and it can't threaten it.