Why did france and west germany start to build a political and economic in europe

They wanted a strong alliance to attack the Soviet Union.- They did not. Where as France did not mind an alliance as much as W Germany, W Germany would never have partnered with the Soviet Union. 

They wanted to protect themselves from another Great Depression.- The Great Dperession Had been over many years before France and W Germany Teamed up. 

They wanted to prevent their two countries from starting another war. This is silly. W Germany wouldn't have joined an alliance to prevent war, if that were there intention. 

Your answer is: They wanted to make an alliance that would rival NATO. Charles De Gaulle could not stand being dependent on the United States for support and trade, and took france out of NATO over the issue of France's developement of nuclear weapons. W Germany wasn't in the smae position, but wanted more independance as well.