Acces Denied with the email link confirmation

Are you sure you set the user permissions so that anonymous users may sign the petition? I mean under:
"admin/user/permissions" ?
This can also be due to your Internet hosts:
When I tested the petition module on (very cheap but) poor quality server, this kind of issue was happening: clicking on the confirmation link would send to a white screen and then tell I had no access...
Have you tested yourself to sign?

Very strange....
If you test on my demonstration site at http://petition.blogopa.net, you will see that it doesn't happen...

Have you check the other access settings of your site?

The function called to confirmed the signature is found at the menu path:
petition/signature/confirmation/+ a few agurments.
If it works normally, you should get a message to confirm that...

Could this menu path be "occupied" by another module or another menu?

What happens if you type in your url:

http://yoursite.fr/petition/signature/confirmation/1/1/1/1 ?

Do you have an access error or a page not found (it should be a page not found)

Well, I think I know what it is the reason...
I will not have the the possibility to update the code before one week or two, but let me guess:
In the petition settings, you chose not to keep the signatures private?

After confirming the signature is confirmed, the user is sent to page 'node/%/signatures' where % is the nid of the petition. This is the page displaying the signatures but because the signatures are kept private, the user cannot see the page.

You can momentarily fix the code.

In the petition_module directory, please modify the petition.module file accordingly:
on line 1737, replace

 $url ='node/'. $nid .'/signatures';
 // empty the cache before routing to the result page
 cache_clear_all();
 drupal_goto($url);

with the following code:

 $url ='node/'. $nid;
 // empty the cache before routing to the result page
 cache_clear_all();
 drupal_goto($url);

on line 1699, replace

 $url ='node/'. $nid .'/signatures';
   drupal_goto($url);

with:

 $url ='node/'. $nid;
   drupal_goto($url);

Then it should work.