My view is that there is commodity software and niche/specialized software. You find commercial solutions for both. But OSS is great for commodity software.
Everything becomes a commodity eventually. There's a lot of niche software that then goes mainstream, gets imitated by others, and becomes important to a wide range of sectors. A lot of that software usually ends up with very decent OSS alternatives. If it's worth having in OSS software form, usually somebody ends up working on it.
A lot of OSS projects are already leaning heavily on contributions from individuals and companies inside the EU. That's a good thing for the EU and something to stimulate and build on.
What the EU should do is keep an eye out for commodity software where it relies on non eu commercial software. Identify key areas where that is risky, e.g. communication software, IOT, or finance. And then stimulate members to switch to OSS alternatives if they exist and invest in the creation/support of such alternatives if they are important. OSS software doesn't just create itself, it needs backing from companies which could use the support in the form of grants.
That could include support for non EU OSS projects. There's nothing wrong with OSS from abroad. As long as this software is properly governed and vital to the EU, the EU should ensure those projects are healthy and future proofed. It should ensure local software companies get the support they need to do the right things here. This should ensure projects that are important don't run out of funding. And the EU can stimulate OSS development into strategic new areas with incentives. And make sure that EU companies that back this are successful internationally. This turns the tables on other countries maybe depending more on EU sourced software. The EU doesn't have to follow; it can lead.