These steps let you install UbisoftConnect into the Compat-data folder for the game which supersedes the broken uplay installation that comes with the game:

1. Install Assassin's Creed Syndicate, choose ProtonExperimental, do not launch it.
2. Download the UbisoftConnect Installer and add it as a non-Steam game to Steam.
3. In the settings for the installer set Compatibility to ProtonExperimental and add this launch option: STEAM_COMPAT_DATA_PATH="/home/[yourhome]/.steam/steam/steamapps/compatdata/368500" %command%
4. Start the installer and keep the checkmark in the box so the app is launched directly afterwards. Wait for it to update then enter your credentials and all. At this point it will not yet have detected the game. Close the launcher.
5. Start the game, if everything went right, it will launch UbisoftConnect instead of uplay and start the game.