Lydie Salvayre beat competition from favourites Kamel Daoud, an Algerian first-time novelist, and French best-selling author David Foenkinos to win the prize.
Born in 1948, she grew up in the southern French city of Toulouse after her parents fled the regime of Spanish dictator Francisco Franco, learning French only when she went to school.
"I am very happy, I'm very moved," Salvayre said with tears in her eyes, following the announcement, made in line with a 100-year-old tradition at Paris's Drouant restaurant.
The author of numerous books, many of her works have been adapted for the theatre and she has been translated into over 20 languages.
Her Goncourt-winning novel is dominated by both the figure of writer Georges Bernanos and the voice of her own mother, Montse, telling the story of the uprising that started Spain's civil war in 1936.
The winner of the prize receives the nominal sum of €10 ($12) but can expect to see sales of around 400,000 in what is considered a literary jackpot for authors.
Sales of Pierre Lemaitre's 2013 winner "Au revoir la-haut" soared from 30,000 to 620,000, according to his publishers Albin Michel.
The prize is one of four important literary awards handed out in France this week starting with the Femina on Monday and the Medicis on Tuesday.
The lesser known Renaudot, also announced on Wednesday, went to Foenkinos for his book "Charlotte", a tribute to a young artist, Charlotte Salomon, killed at Auschwitz in 1943.
Thanks to his 2009 novel "La delicatesse" ("Delicacy"), which was made into a film starring Audrey Tautou, the 40-year-old writer is already one of France's bestselling authors.