Well. So after leaving the thing for a while I came back and did try to install the Moodle 1.9.5. version myself (unpacking the zipped bundle) filling in the required parameters (database, paths...).
Once again there was an enigmatic error message, the config.php file not being accessible (Warning: require_once(config.php) [function.require-once]: failed to open stream: Permission denied in home/parcouri/public_html/lp/lapuerta/index.php on line 33).
I found out that the permissions had been set to 0644 (Is this Moodle itself doing this? Or an automatic thing done by the server?) so I changed it to 0755 and lo and behold: Moodle opened, worked and still works.
So fantastico is not fantastic, I grant you. I didn't install the latest version of Moodle because the server on which Moodle is hosted does not have the php 5.3.2 version. I wonder if I miss a lot not having the latest version.
Anyway, thank you for the reply, which made me have another go at it, and taught me a thing or two concerning permissions.
Cheers,
H. Pelissier