I think the question is "are there any *competent* repair shops?"
I've ended up servicing a number of A4000D boards which suffered more damage than the original fault after going to a "repair" shop in the UK. Least to say, a gorilla wielding a wood chisel and a flame thrower isn't the correct way to carry out SMD work.
There's Amiga Repair Centre in France which is fairly close to you, JJ does a good job. I also do part-time component level work on all Amiga models, international jobs are no problem.
Let me know if you want a price estimate, contact details
here.
As a rough guide, the average cost of most A4000D motherboard repairs work out to be around UKP50 including parts, labour (with full testing) and international airfreight for return. Of course the exact amount depends on the complexity of the job, parts used, etc.
As mentioned, you might be able to repair a few basic things yourself. Check the link above for various hardware guides I've written.