Hi Matthieu,
I agree with you on the diagnostic. However Polylang has nothing to do with this issue as the html markup for nav menus is generated by WordPress and not by Polylang (with the exception of the <img> tag for the flag).
Your theme is Twenty Thirteen. Try adding a page in your menu and go to that page. you will observe the same issue.
Nothing is lost though for people wanting an accessible nav menu for their website as WordPress does allow to use a custom nav menu walker to customize the way nav menu items are displayed. But that requires extra coding. I am aware that some themes use a custom nav menu walker (maybe not for that reason though).
If I added an <em> or <strong> to menu language switcher, I would likely break some themes as themes authors do not expect these markups.