OK.
I installed wordpress locally on my mac by re-downloading everything, and putting it in the right place without modifying anything and it worked.
Similarly I deleted all the wordpress files on my host, re-downloaded wordpress, I did not create a wp-config.php, tried to access install.php : haha. It failed.
My host supports PHP 4.x, 5.x, MySQL… (just one question : what’s “The mod_rewrite Apache module”?).
I still get a 500 Internal server error when I launch the install.php.
I did not write a wp-config.php file because that’s how it worked locally.
I don’t know where is the problem.
Other question : Does the database have to be in the same folder?
Thanks for your help.