There were many factors, not the least of which was that Italy was still a neutral power; it didn't join Germany's war until after Paris had fallen. Hitler tried to convince Mussolini to join the war for months but dropped these demands as the invasion of France succeeded beyond his expectations.

If Germany had brought Italy into the war in 1939, it's likely that the "Phony War" in Europe would have been broken up by quick and undistracted Allied action against Italian positions in Ethiopia and Libya; with Germany concentrating on Europe and Italy still trying to digest Albania, it's unlikely the Axis could have mounted any action across the Mediterranean.

Britain and France had their best units, including divisions of heavy armor, artillery, and air support, concentrated in the north. Had Germany moved its main thrust to the southern front, it would have sacrificed speed and logistical support while leaving the Saar and the Ruhr open to a counterattack. Fielding its army from the north allowed Germany to funnel supplies by rail and road; fielding it through Czechoslovakia and northern Italy would have choked supply, especially since Germany was heavily dependent on horses and mules for much of its logistics.

Further, southern France didn't have the industrial or political importance of Paris, and even a successful campaign there would give Britain ample opportunity to reinforce or withdraw its soldiers.