If the EU wants to arrest someone they can submit an extradition request which the US will approve or deny after reviewing. The EU can also already arrest individuals whom are found to be criminals.

You are suggesting a totally new weapon for EU law enforcement which is to imprison individuals who are not found guilty of a crime because they work for a company that owes the EU money. That sounds a bit insane to me, I think if the EU wants to collect their fine they should find a more diplomatic approach that does not equate to a literal war crime [1]

[1] https://en.wikipedia.org/wiki/Hostage