I'm from France too, and Mozilla is already more known than many others in the Open Source space, and their user base is still huge compared to anything else.
Z0mbie42 is young and did not see when Mozilla was the browser alternative before Google Chrome and stole the show. It is coming back today though because users start to realize the "Google problem".
Now Mozilla is a browser alternative and not a services one. But this is a good example of how unrealistic and not so good it is to want to be a "google" alternative. Today Google is everywhere from search engine (the original google) to collaboration, music, pro apps, video, browsers and so on.
Building an alternative as open source is good but it should clearly not be as monolithic as Google is.
Now it's complicated because users want a more integrated experience and open source developers that manage to grow their tool in a specific area dont have that much time and funding to better integrate so it's slow.
Also copying as is Google as Open Source is also not the solution. What about privacy. I believe end to end encryption is key. There are advancement in this area (the project cryptpad.fr we work on is one of them). What about decentralization ? There are tools building up in this area like mastodon or peer tube.
I wish Open Source can come out with an alternative, but it will need to be an integration of solutions, and not only a monolithic solution. Check out Framasoft.org for an incredible list of open source services they host.
Ludovic