Germany's annexation of Alsace-Lorraine was a source of ongoing resentment by the French. As was France's loss of its status as the dominant land power in Europe. War was not inevitable, but the unresolved issues from the Franco-Prussian war ensured that the two dominant continental powers would be enemies. France's desire to be secure against Germany leads it to form an alliance with Russia, which then puts Germany in a terrible situation of being surrounded by two great powers. You're right, it's not like two people held a grudge for 45 years, but the war made it likely that the two nations would fight each other again.