To handle multilingual menus, there are several options.

Module displayed only for a language

Add a menu to a module and filter module by language

• Multilingual Module

Use language files to translate labels

You can use the standard string translation process

• set your menu option name in admin-> menu in English
• set the user module title in the admin -> modules panel in English
• add in lang/your_language/language.php, the list on translations

But the URLs will not be translated. English should be the reference language, the same way it is the Smarty templates.

Check language and show alternate menu

The best way to do this is using the Module menu and set the Language parameter in Module Settings Parameters to display the menu when you select a language for the current session. You will need one menu for each language on your website.

Alternatively you can add the following script in Site Identity:

{if $prefs.language eq "en"}
{menu id=43 css=y type=horiz}
{else}    
{menu id=1 css=y type=horiz}
{/if}