No one really knows for sure what Petain's thinking was, but the French armies were in a hopeless military position at the time that Petain came to power in June 1940. He believed that the Germans had won the war, that Great Britain wouldn't be able to resist the Germans fighting alone, and that he needed to make a deal with the Germans on the best terms he possibly could.
Petain is known to have deeply sympathized with the French people and the suffering they endured in the First World War, and on more than one occasion as leader of the wartime Vichy government, he made dishonorable agreements with the Nazis to make life easier on the people. One of his advisors rebuked him for this, telling him "you care more about the French than you do about France."
Politically, Petain held to a philosophy similar to Franco; a Fascist economic system with a conservative Catholic bend; he put this into place when he came to power. He may have seen the French defeat as a way to remake the country into what he thought it should be. Indeed, he blamed the defeat on France's turn toward liberalism.
All in all, he probably hoped that his ideas would take root in France, that his deal with Nazi Germany would keep France out of the remainder of the war and protect its people from the worst of it, and that the war would end in a way that France would not forever be a German vassal.