My 2 cents:

• Use jQuery toggleClass : http://api.jquery.com/toggleClass/
• Use camelCase : currencycode -> currencyCode etc.
• Use English everywhere : 'monnaie' should not be there
• Booleans are awesome

        if($myCurrencycode == $initCurrencycode) {
            hasChanged = false;
            console.log(hasChanged);
        } else {
            hasChanged = true;
            console.log(hasChanged);
        }

should be

   hasChanged = ($myCurrencycode != $initCurrencycode)
   console.log( hasChanged );

My 2 cents:

• Use jQuery toggleClass : http://api.jquery.com/toggleClass/
• Use camelCase : currencycode -> currencyCode etc.
• Use English everywhere : 'monnaie' should not be there
• Booleans are awesome

        if($myCurrencycode == $initCurrencycode) {
            hasChanged = false;
            console.log(hasChanged);
        } else {
            hasChanged = true;
            console.log(hasChanged);
        }

should be

   hasChanged = ($myCurrencycode != $initCurrencycode)
   console.log( hasChanged );

• Finally,

if(!$menuDropdown.hasClass('hide')) {
  $menuDropdown.addClass('hide');
}

can be replaced with $menuDropdown.addClass('hide'); it will not add the class multiple times.