I would love for such a fund to invest very liberally in these companies, on the condition that anything it funds must be free and open source - public money, public code! The only way to take down these giant US companies is to work together, and the most effective way to work together is to release everything in the open in such a way that anyone can build on top of it.
If the money just gets funneled into these companies so they can build their own lock-in, the EU would be recreating the same dependency on a few small companies that happened in the US. It wouldn't increase productivity in the long run, it would instead substitute dependency on a few US companies for a few EU companies.
But, if they invest in open source software, it could spur innovation not only in the companies that are directly funded, but also thousands of other companies throughout the EU that would now have common infrastructure that they can build on top of.
I can highly recommend Mythic Beasts (UK).
There is no upsell or variable pricing and they make money by charging a flat rate on top of the cost from their supplier. See this blog post for more info