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London's benchmark FTSE 100 index of leading shares rose 1.05 percent to 5,716.79 points, the Paris CAC 40 gained 1.09 percent to 3,260.27 points and Frankfurt's DAX 30 added 1.32 percent to 6,301.91 points.
Asian markets and the euro also rose on Tuesday, boosted by better-than-expected Chinese economic data while sentiment was supported by a successful French bond auction.
However, eurozone debt woes persisted as Standard & Poor's's downgrade of nine countries, including France, was followed by a ratings cut for the bailout fund set up to help under-pressure European economies.
Wall Street was shut on Monday for a public holiday and reopens later on Tuesday.