The ceremony was attended by Law's parents, Peter and Maggie, who divide their time between London and Saumur in western France, where they run a drama school, and director Anthony Minghella.
"Your immense success has not been handed to you on a plate. It has been the product of hard work," Errera said, presenting Law with a medal.
"I am speechless," the 34-year-old actor said. "My mom and dad have lived in France for 15 years so really it is a country I share as my home."
Law's films include "Alfie," "Cold Mountain" and Minghella's "The Talented Mr. Ripley."
France presents Order of Arts and Letters awards to French nationals and foreigners deemed to have significantly contributed to the country's cultural inheritance. Previous foreign recipients include Uma Thurman, Bruce Willis and David Bowie.