I initially thought it was because my dropbox was install also on a windows system, and the difference between file system (ext4 and ntfs) may cause dropbox not being able to sync.
I have uninstalled windows dropbox and have reassociated the debian's one so it has downloaded a fresh version of my files. This part was ok. But after I had to suspend sync on restart it in order for dropbox to detect change (new file for example).
And after a reboot, the sync icon was ever pending without doing nothing. I have no idea to investigate.