For centuries, they were the two most powerful countries in the world or at least in Europe.
They both wanted to be "The Big Boss" but they never succeeded at dominating each other.
Everytime the French tried to take over Europe or some parts of the world, the English were there to stop them, and everytime the English tried to take over Europe or some parts of the world, the French were there to stop them too.
Before the 2 world wars, England had an adantage by having by far the greatest Empire, but the French had by far the second greatest !
In WW1, England and France fought side by side and won with some help from the USA.
In WW2 however, France was defeated and England resisted and finally won with a big help from the USA.
Finally, the USA became "The Big Boss" and England chosed to make everything like the USA.
France, however, never really trusted the USA since the Americans had betrayed them during the Napoleonic Wars, and even if the USA later saved France's a*s in WW2, the French decided to become some sort of allied counter-power, and for doing so, they spread their influence in the European Union.
Now, the French see the English as friends, but also rivals who can't be counted on since they will always follow their boss, the USA.
The English see the French as the crazy leaders of the evil European Union, and even if, deep into their heart, they know they like the French and greatly respect them, they constantly bash the French.
They bash the French so much that they are now convinced the French are just a bunch of arrogant a*sholes who never had any importance and who never won any war...
It's pretty stupid, since France has an amazing and very influent culture and has an as great military history than the UK... But since France lost WW2 and needed help in WW1 (even if France was the major winner of WW1), they declare the French always surrendered in every war... Just nonsense.
By the way, the French are very well seen in the world. Only the Brits, the Americans and the Chinese (since Beijing 2008) don't like them, mostly because the French like to do things their own way and don't like to shut up even in front of more powerful countries than France (see War in Iraq in 2003...)
The English have a good reputation, mostly because of their amazing music, but are often seen in Europe as the pets of the USA, unfortunately...