What was Franklin D. Roosevelt's political philosophy?
I would describe Roosevelt's political philosophy as "pragmatic." He was not a strong liberal by today's standards nor was he a conservative in the vein of Herbert Hoover. Instead, he tended to try to achieve as much as he could through whatever means seemed likely to work.
We can see that he was not conservative from the New Deal. He injected the government strongly into the economy in a way that no conservative would have tolerated. At the same time, however, he was wary of deficits, cutting back on the New Deal after his first reelection. In addition, he was willing to compromise his principles in some areas to get what he wanted in others. For example, he was willing to allow New Deal programs to discriminate against African Americans in order to get support from conservative Southern politicians.
So, I would say that FDR was a pragmatic leader who leaned to the left in his political philosophy.