Why did Bismarck want to force the French to fight against Prussia?

Bismarck's ultimate task was to create a united Germany under the leadership of Prussia. In other word the German Empire.

The first step on this way was to get rid of Danish sovereignty upon the German Duchies of Schleswig-Holstein, what he did in alliance and with active participation of Austrian Fleet and Army. It was a real war of aggression disguised as a war of liberation, in order to obtain the consent of the other German States.

The second step was to annihilate the Austrian political predominance in Germany, what he did by provoking Austria to the war of 1866.

The third step was that of promoting a political union between the many States in which Germany was still divided in that time. But those States were somewhat suspicious of Prussia fearing that they would be simply be "absorbed" had they agreed with Bismarck's proposals.

France played a certain role in nourishing their suspicion, because a strong, united German nation wouldn't have suited its interests.

So, in order to raise the German national patriotic spirit and popular indignation against the common age-old enemy, Bismarck managed France to declare war on Prussia.

That led to an immediate military alliance of all the German States with Prussia to fight the "aggressor".

The German Empire was proclaimed on Dec. 10, 1870 and the King of Prussia was acclaimed German Emperor on Jan. 18, 1871 in the Hall of Mirrors at the Palace of Versailles.