Cotillard, the star of the acclaimed 2007 film "La Vie en Rose" on French singer Edith Piaf, entered the cage and held a banner proclaiming: "I am a climate defender."
She joined Greenpeace activists all dressed in red.
"There are people who have the courage to defend our planet and who put themselves into great trouble," she said, calling the detention "absolutely absurd and crazy".
The symbolic protest was staged in the heart of Paris at the Palais Royal complex, where the state theatre Comedie Francaise is located.
The so-called "Arctic 30" were detained when the Russian Coast Guard boarded their Dutch-flagged Greenpeace vessel after several activists scaled a state-owned oil platform on September 18 in a protest.
Russia has since put the 30 people in prisons in Saint Petersburg pending trial after moving them from the Arctic Circle city of Murmansk.