I need to change the hosting server for a website referenced in France. If i take a hosting server in Belgium (google gce eu-west-1) would this affect my site natural SEO ?
If you do everything correctly, nor you neither your visitors feel any affect.
Everything correctly means: french geo-TLD (.fr), content in french language.
Regarding performance issues, like routing, DNS query etc. - you could study the infrastructure of some CDN services and make use of those, who have servers staying in Belgium and France. But inside of continental West Europe (Poland-Portugal, Norway-Italy) such differences are negligible, if you don't run really have loaded site.
There's a slight advantage to having your webhosting in the same region as the customers that you're targeting. For users in France, a webhosting company in France is likely slightly faster than a webhosting company in another part of Europe. It might even be substantially faster than a webhosting company somewhere else further in the world.
Google has stated that page load speed is a ranking factor. And so anything that can boost the site's performance will help your rankings.
Because Belgium is quite close to France, the latency in page speed might only be milliseconds. And so this might not be enough of a factor to prevent yourself from switching servers.
Does Google target users in a country with websites hosted by servers in that same country? This last part I'm not sure about.
Ya it's effect.... because if you take your hosting server in Belgium instead of France then your website is little bit slowly open...it is happen because if anybody search your website in France then the data receive by the server in Belgium and come to the France...so it's effect SEO. because people would never search the slowest websites...