Is there a way to get the URL of the localised version of a product variant?
Try using this code:

{% set variantID = craft.request.getParam('variant') %}
{% set locales = craft.i18n.getSiteLocaleIds() %}

{% for locale in locales %}
    {% if variantID is defined %}
        {% set localisedEntryUrl = craft.commerce.variants.id(variantID).locale(locale).first %}
        {% if localeEntry.locale == locale %}
            {{ localisedEntryUrl.getUrl() }}
        {% endif %}
    {% endif %}
{% endfor %}