At first, download and install the latest version of Origin at www.origin.com/download (and make sure you have your Origin account ready as well)
Close the origin client and go directly to you origin folder C:\Program Files\Origin Games. Run the origin.exe in this folder with a rightclick -> run as administrator.
If that won't work I recommend to delete your Titanfall folder out of /OriginGames and re-install and update the game after. This should solve your issue.
Please keep us updated.
Basti
