Click the text label ("Pays", "Ville" etc) and select the value. That records it in the catalogue, and you can then use CtrlS / CmdS to save the metadata back to the files.
The grey italic values for Sublocation, City, State, and Country indicate they have been provided by LR's automatic address suggestions but not confirmed by you. If you do nothing, they will still appear in the recorded metadata of exported versions of the photo (unless you select the option Remove Location Info in the Export window).
As John Beardsworth described, you can "commit" these values (turn them to regular white font) by clicking on the labels and selecting the current values. Normally, there's no need to do this, except in one case: If you want to edit one of the fields but not the others, you need to commit the values first, otherwise the other fields will be cleared.
If you end up with many photos with unconfirmed locations, the Any Tag plugin has a free-to-use command Commit Locations that will automatically confirm the location fields of an entire batch.
A lot of people have complained about LR's behavior -- please add your me-to vote to this topic in the official Adobe feedback forum: Lightroom: improve control over reverse-geocoded Location metadata | Photoshop Family Customer Community