Yeah, there will be immediate pain but if EU competitors can spring up because the American software giants are disadvantaged it'll slowly erode the reliance on US's software.
It's also a matter of two advantages the USA has:
1. being a homogeneous market culturally-linguistic, there are dozens of countries with very different cultures and languages in Europe, it's not as easy to scale continent-wide as it is to scale country-wide in the USA.
2. exhuberant privilege of the USD, it gives a major advantage on capital markets where capital is sloshing around in the economy, it's much easier to find billions of USD parked somewhere wanting to get better returns. The EU doesn't have this privilege, investments need to be more conservative.