Perhaps I'm not getting it as should, but as far as I got it, CloudFlare should use local(geographically) servers, relative to the user, to deliver the content. But instead, I'm getting all the time US servers(I'm in Europe).
How do I fix this?
You're likely using a geolocation service to determine the location of the IP address. This may not accurately tell you where the server for that IP is located - Cloudflare owns large IP blocks. These blocks will be registered to them somewhere in the USA and perhaps the servers for these IPs are even located there.
However, if they move a B block in that range to Europe, it means a 1 digit difference in the IP changes the location completely. 188.8.131.52/12 for example is a huge range of IPs. That's over 1.4 mil IPs split into around 64k B blocks (excuse my napkin math).
The ISPs would be aware of an edge router's location but IP block registration databases wouldn't. Do a ping command and use response time and TTL to measure distance. TTL will tell you how many routers your ping has bounced through - even if response time doesn't waver much you'll be able to see that it's gone a greater distance. For further detail, a tracert command (Windows) will also reveal more about location by attempting to resolve and ping each individual router along the way. Done from different origin IPs, you'll also be able to see if your ISP is doing any redirecting for Cloudflare in order to shorten distance travelled.
Edit: Another answer has pointed out you can also use yourdomain.com/cdn-cgi/trace in order to get a debug output with the 'colo=' code indicating the location of the server being used. Example output:
uag=Mozilla Compatible Agent
colo=LHR // Datacentre location