Hi Sharann,
You are right: one fundamental difference between the French and British legal systems is the constitutional system. The
French Constution is codified (it has been written down), but as far as I know, the British constitution is unwritten.
Julielai mentioned the idea of a federation. Europe is far from becoming a federation with a single legislative code. This is because federations, like the USA, are normally single nations made up of many states; Europe, on the other hand, is a whole jumble. In the EU there are nations which aren't states, states which aren't nations, and states which are also nations (nation-states). The USA works as a federation with a common law because Americans feel that they are part of one nation. This would be very difficult to achieve in Europe, because we are all so different. In fact, the slogan of the EU is 'Unity in Diversity', meaning that we are united by our differences.