So I just bought a Hegel H390 and

Jealous of that amp!
I've heard Dyns are a great match for Hegel. And if you've never had dyns you should give 'em a day in court!

Definitely hear the Fyne line

I can tell you, without a doubt,  BUY something better than even 12 gauge zip cord....  amazing difference.    you don't have to spend a lot either.   Something like MORROW sp4 or sp5 for under $500 will make a very noticeable difference.

Just buy these https://www.usaudiomart.com/details/649764283-salk-song3-speakers/

i demo’d speakers going up to $6k and preferred the Salks. I’ve upgraded to Cube Nenuphar Mini’s and at 1/3 the price (when new) the Salks more than held their own. I’ve had some people listen to both who actually prefer the Salks and I can see why because they dig deeper and the RAAL tweeter is amazing. Fantastic match with you beautiful Hegel. 

I owned the h390 and had it paired with the Triton Reference speakers.  Was very pleased with the sound.  I found the Triton to be an excellent value. The company motto is "We make High End Affordable".  I think they retail in the $7000 range in the U.S.  Encourage you to check them out before you make the final decision.  Also, don't rule out buying used.  There's a lot of terrific bargains out there.  Got to love "like new" at half the price?