The bronze hands of the sculpture were daubed in red paint to signify blood, The Daily Mail reported.
The statue also sported the initials "R.H." believed to be in memory of Rudolf Hess, the report said. Hess, Adolf Hitler's deputy, flew to Britain at the height of World War II apparently to try to make peace but Churchill, then prime minister, had him arrested and the war continued for another four years.
Many French hold negative views of Churchill, the newspaper noted.
Some call him a war criminal because he ordered the Vichy French fleet scuttled in Tunisia rather than allow it to fall into the hands of the Third Reich. Others remember Churchill ordered the Allied bombing of occupied France in which thousands of French citizens died.
However, the strongest reaction from French people was anger at the attack on the statue, which is near the Champs Elysee.