did they turn away from it to fight the French head on? I assume it's cause they were trying to get that knockout blow as soon as possible, but if they had occupied Paris how different would the remainder of the war had been?

The city had been abandoned, as you mention, by the French government, so as a center of French leadership it's value had greatly decreased. Moreover, General Gallieni was rallying reservists and regulars to defend the city, and the French 6th and 9th armies, as well as the BEF, were in fairly close proximity. Attacking it would only have meant bloody, urban street fighting, and an increased gap between the 1st and 2nd armies. So, even if (and that's a very big IF) the Germans captured Paris, it would have been incredibly costly, and would have done little to improve the German position.

Holger Herwig's book on the Marne is worth a read for this.