The origin of the longterm tensions between France and England are understandable given the two nations' intertwined history, but what's the deal with the enmity between France and Germany (which, like with England, has eased since WWII)?
France was a major european power in the middle ages and later. There was no united German state, but the Holy Roman Empire, in which the German states were sort of organized. On the border between the two spheres were the Provinces Alsace and Lorraine. They were on the border, but they were more German and in the Holy Roman Empire. France conquered these provinces to gain more influence in Germany.
The Germans then wanted to get these provinces back and saw France as an enemy who took land from them. But it didn't happen until 1871 when Prussia won the war against France and annexed Alsace and Lorraine "back", even after they were a long time (a hundred years or a few hundred years) in France. Now France wanted these provinces back and saw the now unified Germany as an enemy. This went on until after first world war, when Germany had to give Alsace and Lorraine back to France because of the Treaty of Versailles.
This treaty also included huge reparations that had to be given to France. Germany couldn't pay them in 1923 and France occupied the Ruhrgebiet (also called "Ruhrbesetzung"). The Ruhrgebiet is a highly industrialized area in West Germany with lots of coal mines. They occupied it and took the coal as payment which increased the hate of the Germans on the French. The Treaty of Versailles also included that France occupied the Saargebiet, a German Province right at the border to France. So you understand the the Gemrans were quite upset about the French after the first World War.
There were people who wanted to cooperate wih France to reduce hate, for example German Foreign Relations Minister Gustav Stresemann and his French counterpart Aristide Briand who wanted to strengthen peace between the two Nations. They were together awarded with the Peace Nobel Prize in 1926 for their cooperation and try to make the two states not longer enemies. When Hitler came to power he propagated new hate against the French and in 1940 the two Provinces were reintegrated into Germany after France was defeated.
After the Second World War the French got the provinces back and occupied a part of Germany together with GB, USA and the Soviet Union, called the four "Besatzungszonen"(Occupied Zones).
In 1963, West Germany and France began the Élysée Treaty or the German-French Friendship Treaty which aim was to reduce tensions between the two states. The two countries should work together in for example political and economical issues and meet often to speak about problems. Since then, Germany and France are more and more "Friends".
Source: The German book "Die Schuld am deutschen Schicksal: Wahrheit als Waffe gegen Lüge" by Gerhard Krause, published in 1973 by Schütz Verlag. The book itself is about the circumstances that lead to the first and second World War and Germanys role in it.