When I activate Gzip I find that my site is slow, as if Varnish was not doing its job.
Gzip compression generally has no negative impact on Varnish's performance. Varnish will store the Gzip'ed content without performing any modifications to it and will deliver the same content to the client.
Given that Varnish actually can serve this content as a hit, it should be really fast.
Can you send me the full
varnishlog output for the slow transaction? This will show where the delay is located and whether or not Varnish can actually cache the response.