Coogan, who starred in, co-wrote and co-produced the film, was nominated for a Golden Globe for his screenplay. The film tells the story of Philomena’s search for her adopted son.
She and Coogan are campaigning for the release of 60,000 adoption files held by the Irish state, churches and private agencies.
As an unmarried mother in Ireland in the 1950s, Philomena was put into a convent as a “fallen woman” and forced to give up her three-year-old son.
“I am honoured and delighted to have been in the presence of Pope Francis, she said. “As the film portrays, I have always put great faith in the church and the good will to put the wrongs of the past right.
“I hope and believe that his Holiness Pope Francis joins me in the fight to help the thousands of mothers and children who need closure on their own stories.”