European stock markets rose sharply at the start of trading on Tuesday, building on sizeable gains won a day earlier when shares were boosted by hopes of a deal to resolve the eurozone debt crisis. At the open on Tuesday, London's FTSE 100 index of leading shares rallied 2.08 percent to 5,195.22 points, Frankfurt's DAX 30 surged 2.94 percent to 5,502.89 points and in Paris the CAC 40 jumped 2.34 percent to 2,926.30 points.