Actually I would say the need for sensible regulation of the financial markets and a more serious approach to fully funding infrastructure and the social safety net are lessons we could take away from his Presidency. An FDR era law called the Glass-Steagall Act, which separated investment banks from regular banks, among other things, was repealed in 1999. This, in part, is what allowed the complicated derivative schemes and risky lending that led us to the Great Recession we are still struggling to emerge from.
I would argue that there is nothing that the government today can learn from the experience of Franklin Roosevelt during the Great Depression. The world today is too different from FDR's world and the things that he did would no longer have much of an impact today.
The main reason for this is that most of the things that FDR did in the New Deal remain with us today. Today, it would be much more difficult for the government to do anything to really kickstart the economy because the government already does so much. Government programs are not a new thing today as they were during the Depression so they would not have the same effect.
In addition, the political scene is much different today. For one thing, FDR did not face the kind of deficit and debt problems that we now face. He could simply throw lots of money at the problems of the Depression. The US can no longer afford to do that.
For these reasons, I think there is very little to be learned from FDR's actions in the 1930s.