It wasn’t a century, it started in 1871 when Germany reunited.
The French didn’t want to conquer Europe in 1871. Napoleon III foolishly thought he could teach the Prussians a lesson & provoked a war with them — and proceeded to lose everything: the war, his throne, Alsace-Lorraine, and gain a hostile, United German state on France’s border.
The French wanted Alsace-Lorraine back ever since its defeat in the Franco-Prussian war in 1871.