Ok, it works for query string now.
I saw that $request_uri already contains query string.

location ~ ^/purge(/.*) {
fastcgi_cache_purge FASTCGICACHE "$scheme$request_method$host$1$is_args$args#$http_range$isAjax";
}

I use $1$is_args$args like $request_uri. But special characters are probably endoded during the location regex ?
So now, hox to deal with special characters (é, è...) ?