Currently both France and Germany share a common currency, which is the Euro. The Euro is the single currency for 20 European nations and has the same value and exchange rate across all nations; it can also be used interchangeable in all countries.
After the Second World War, France and Germany made an effort to integrate their political and economic systems in order to avoid a repeat of the destructive conflicts that had ranged on the continent for centuries. The E.U itself traces its beginnings from the European Coal and Steel Community (ECSC) and the European Economic Community (EEC). So France and Germany had technically been integrating for over 40 years before the formal establishment of the E.U. The E.U itself was founded in 1993 at the signing of the Maastricht Treaty, which has led to deeper economic and political integration between the two countries. The Germans had the Deutsch Mark and the French the Franc before they both adopted the common Euro currency. The German Mark had always been stronger than the French Franc owing to the larger size and strength of the German economy.