JetPack mobile theme does not switch language (Polylang)

Greetings to all!

On a WP site I use Polylang (Version 1.7.12 ) to switch between 2 languages (English and French). It works fine on computers.

To make the site mobile-friendly I use JetPack (Version 3.8.1).
When on an Android mobile phone I change language, the content changes, as it should do. However, the menu does not change, it remains French all the times.

I would guess, that something should be changed at JetPack, as all works fine on PC, with another theme (Dusk To Dawn, also by WordPress.com).

The site is self-hosted (at DreamHost).

http://watsu-wata-test.int.world

How may I make the menus change on mobile, as they do on PC?

Thanks a lot,

Tamas