If they want European the choice is the EJ200 that's on the Eurofighter. It's a little less powerful than the US one they're using, probably why they choose the is one. But apparently has room to become more powerful if they take on additional design work.
The original variant (A) of the F-14 was a turd because they built the aircraft before the actual intended powerplant was available. The engine it got was underpowered and temperamental and resulted in flameouts.
There's been several other aircraft that have been designed and built and then had the program scrapped because the engine to match the airframe never actually made it through development and/or certification.
If you start designing an airplane before you have a proper powerplant selected, it's probably gonna fail.
The others still use European software for cockpit display, fuel management, on-board vehicle systems, Euripean made rear fuselages, and ejection seats.