The director of the blockbuster space film "Gravity" wrote the open letter to Pena Nieto, in which he thanked Pena Nieto for his congratulations on the best-director win at this year's Oscar.
But Cuaron made it clear in the letter he doesn't agree with the way the constitutional reform was passed last year. The reform allows private companies to drill for oil and hold concessions for the first time since the oil industry was nationalized in 1938. Enabling legislation must still be passed.
Cuaron posed 10 questions to the president, including how Mexico would protect its environment, fight endemic corruption and reign in the power of private oil companies.
"The world's multinational oil companies have as much power as many governments," Cuaron wrote. "What measures will be taken to keep our democracy from being taken over by illegal financing and the other methods of pressure by powerful interests?"
"In a country with such a weak or non-existent legal system, how can you avoid large-scale corruption?" he wrote.
Pena Nieto's office had no immediate response to the letter.
The energy reform has already drawn concern because it seeks to encourage the development in Mexico of fracking, which involves pumping chemicals and water underground to break open shale rock formations.
Other people fear a return to the days when foreign oil companies made fortunes in Mexico, while leaving the country with little benefit.
But state ownership over the last seven and a half decades have neither ensured prosperity for Mexico, nor provided low gas and oil prices. A bloated union, corruption within the state-owned oil company and the government's dependence on oil revenues to fund public spending have reduced any benefits that might have trickled down to the average citizen.
Pena Nieto promised the reforms would provide cheaper electrical rates, in part because Mexico now imports significant quantities of natural gas.
But Cuaron's first question was one that many Mexicans have been asking. "When will prices for gas, gasoline, fuel oil and electricity come down?"
While once uncommon, Mexican entertainment figures have increasingly been taking political stances, or supporting political, social and environmental causes.