During the Hundred Years War...?

"During the Hundred Years War, Joan of Arc became a patron saint of France."

Saint Denis is the Patron Saint of France.

Joan of Arc was canonized a Saint in 1920.

"France at that time was roman catholic. england protestant."

England was Catholic during the Hundred Years War. There were no Protestants until the 16th Century.

The Church of England split from Rome under Henry VIII, in 1534. But neither England nor Henry VIII were Protestant. England actually turned Protestant under the reign of Edward VI. All of that happened long after the Hundred Years War, which ended in 1453.

"Question: Which side does god really help?"

Those with the biggest battalions. God had nothing to do with it.

If we are to say that God helped either side, then he must have helped one side at one point in time, like Henry V at Azincourt, and then helped Joan of Arc against his heir, Henry VI. But that doesn't make sense.

It would be reasonable to assume that God is omniscient. So why would an omniscient being change it's mind?

The Hundred Years struggle was once a conflict among 2 families of French origins, the Valois and the Plantagenets, who desired the crown of France and the possesion of the territories of the west of France (Normandy, Anjou, Aquitaine...). So the wrestle took situation in France and no, France did n't invade England or attempted to.

there is only one God..so answer is to whoever believes in him and conducts themselves in a pious manner