if the project name is unique, yes it is possible : search your project by name instead of searching by id
use this rewrite rule :
RewriteEngine on
RewriteBase /
RewriteCond %{REQUEST_FILENAME} !-d # not a dir
RewriteCond %{REQUEST_FILENAME} !-f # not a file**
RewriteRule ^(.*)$ projet-in.php?name=$1&%{QUERY_STRING} [NC,L]
this way, when the user goes to http://foo.fr/projectName
apache will theat the request as http://foo.fr/projet-in.php?name=projectName
so you will get the project in GET parameters in PHP
your new php code will be
<?php
$db = new Database();
$project = $db->findByProjectName($_GET['name']);