The EU spends plenty of grant money on FLOSS. It’s part of the general Horizon grants, there’s a bug bounty programme (as replacement for the hackatons which didn’t work as well as imagined), and last but not least the EU publishes lots of software as FLOSS.

You don’t want to make that stuff contingent on big tech misbehaving. The fines go into the general EU budget but the EU doesn’t get to keep it, membership fees are lowered in the next year by the same amount thus the windfall goes to member state’s budgets.