Mass-effect – use the Xbox One controller to play the PC versions of the Mass Effect games

Mass Effect 3 does not support any other input than mouse and keyboard on the PC, so there is no official way to use an Xbox 360 controller on the PC. See for example this thread on the official forums where a Bioware employee states that the inability to use a controller is intended.

Update

Yes, drivers have been published that will allow you to run on PC, hence, no need for any third-party software! [Source]

You can download the drivers for different build by using the links below or from Major Nelson's post I linked above as source.

• PC Drivers for Xbox One Controller (x86)
• PC Drivers for Xbox One Controller (x64)

Original dating back before 6 June 2014

No. The communication protocol the One controller uses is different from the communication protocol the 360 controller uses. This was needed to make several improvements such as reduced latency and more support for state messages for giving the console more control over the controller's state (it will put the controller in a low power state if you are not holding it).

But as you noted, all these improvements come at a cost. Until the time that someone comes up with a driver for the controller to be used on PC, there is nothing you can do. As X Padder relies on the protocol in use, it too won't be able to solve your issue. That being said, there supposedly is already a driver but because the protocol is likely protected by a patent, the driver would infringe on it. You can read some about it on this US Gamer article.