I've manage to do it thanks to this link provided by @mu3 in the comments. Here is the Apple Script :

activate application "SystemUIServer"
tell application "System Events"
    tell process "SystemUIServer"
        -- Working CONNECT Script.  Goes through the following:
        -- Clicks on Bluetooth Menu (OSX Top Menu Bar)
        --    => Clicks on device Item
        --      => Clicks on Connect Item
        set btMenu to (menu bar item 1 of menu bar 1 whose description contains "bluetooth")
        tell btMenu
            click
            tell (menu item "Beats Solo³ de Anthonin" of menu 1)
                click
                if exists menu item "Connect" of menu 1 then
                    click menu item "Connect" of menu 1
                    return "Connecting..."
                else
                    key code 53 -- Close main BT drop down if Connect wasn't present
                    return "Connect menu was not found, are you already connected?"
                end if
            end tell
        end tell
    end tell
end tell

All you have to do is replacing "Beats Solo³ de Anthonin" with your device name, and if your computer isn't in English, replace "Connect" with its translation in your language.

Hope this helps :)