Hello. On 02-02-2016, sdayman indicated above a quite clear process to activate free https and free Cloudflare:
1) I went to Cloudflare and added my domains.
2) Cloudflare pulled all the DNS data from DreamHost.
3) I updated my WHOIS info to use the Cloudflare Name Servers as instructed on my Cloudflare account.
4) Cloudflare detected this and then started working.
I am chickening out. If this can be of use to anyone here, I am starting to move and post the steps here.
This morning I went to the Dreamhost control panel and unplugged Cloudflare from the domain abeille-cyclotourisme.fr, hosted by Dreamhost and, so far, protected (proxy-ed I presume) by Cloudflare via the Dreamhost control panel. Nothing of significance happened. I will be waiting like that for possible horror stories for 48 hours.
Since I have a Cloudflare account, with (now) no domain on it, I visited Cloudflare, Dreamhost (host) and Bookmyname (domain name registrar). Following the quoted lines of sdayman,
1) "I went to Cloudflare and added my domains". Seems easy to do, I tried it with my bare hands.
2) "Cloudflare pulled all the DNS data from DreamHost". Yes, they did that to me and more, seems easy even to me.
3) "I updated my WHOIS info to use the Cloudflare Name Servers as instructed on my Cloudflare account". Cloudflare gives precise instructions. I checked feasibility of implementation with Bookmyname. Seems easy to do even by me (did not do it though). I then cancelled the Cloudflare registration process. So the website is currently no longer Cloudflare enabled.
4) "Cloudflare detected this and then started working".
After all, this seems feasible even to me. The website would be run with the help of not three but four companies: Bookmyname direct for domain name (for pay), Dreamhost direct for hosting (for pay), Google for mail direct but through Dreamhost control panel (free, maybe due to Dreamhost contract with them) and Cloudflare direct if I implement that (for free). A lot, but doable.
48 hours from now, I intend to implement free https on the Dreamhost CP and post news here. Then... maybe... Cloudflare again.