We are on Sitecore 7.1 (rev. 140324) and need to use WFFM with MVC.
Therefore I would like to check if Sitecore 7.1 (rev. 140324) supports WFFM with MVC.
MVC support is available from WFFM 2.4 rev.140923 which is compatibility with Sitecore 7.2 Initial Release or later only. This version comes with Support MVC 5.
In case if you would like to find the some documentation on applicable support, please refer to release notes at https://sdn.sitecore.net/Products/Web%20Forms%20for%20Marketers/Web%20Forms%20for%20Marketers%202,-d-,4/Release%20Notes.aspx
Web Forms for Marketers module 2.4 rev.140923 version of the module runs on Sitecore 7.2 rev. 140228 and later.
This version Support MVC 5 and WFFM functionality works on Sitecore MVC layouts.
So you need to move to Sitecore 7.2 version atleast.