Bonjour,
If I may add to and expand on the above suggestions:

Make absolutely certain, before you do any of the following, that you have pertinent and descriptive descriptions and keywords entered in the Global Configuration > Site > Metadata Settings. So many times I have seen Google search results with the default Joomla! values
1) Set up a Google Webmaster Account (GWA)
2) Verify the site with the GWA
3) If your hosting provider does not offer this service (mine does),
go here and create a 'sitemap' and then submit the resultant file with GWA
4) Create a Google Analytics Account (GAA), get the resultant generated code and place it in the index.php of the
DEFAULT TEMPLATE (and any other templates you may have "assigned") just before the closing </body> tag
5) If you and your site qualify, set up a Google AdSense Account and get
this extension,
this extension, and
this extension and install and set them up.
Your mileage may vary, but the last site I set up was indexed within 3 days using the above. And a recent change to the meta tags was refreshed and displayed within about the same time frame.
Cheers!
Lyle