Thanks for your answer.
Yes I think tried all the configurations in the customizer and none makes the mobile version menu like I want it.
I wanted all the page titles in the menu to be written in white (which is not happening in the mobile version), and underlined when hovered (which is happening and working fine in every version).
I have an issue with the mobile version of this lay-theme website: http://contour-studio.fr/ on every browser I tried (chrome, safari, firefox).
On mobile, in the menu, the inactive page title "Le studio" is written in black.. on a black background ! It only appears white again when the mouse goes over it on laptop or when you tap and click on it on a mobile.
I was trying to figure out what was going on and I discovered that this problem appeared also in the desktop version when I selected the "Default" option in [Primary Menu -> Text Format]. Instead, selecting just the above option "--SELECT--" as the text format solved the issue (for the desktop version).
By the way , thanks for this great theme and for the support !