Operation Dragoon, in the south of France, happened after three important events. Firstly, Operation Overlord, The invasion of Normandy succeeded in creating a beachhead on June 6th. Secondly the Soviet Operation Bagration in Byelorussia eviscerated a huge chunk of the German army from June 23rd into August. Thirdly, Operation Cobra, broke the German containment of the beachhead on July 25th and put another large slice of the German army in headlong retreat with heavy casualties. This period of the war, June 6th to August 14th is when the German army suffered it's highest casualties of the war and sealed it's fate. Operation Dragoon happened on August 15th, 1944, so while it's important the other campaigns were more decisive.

In addition to timing, let's explore the geography and logistics of Normandy, Italy, and southern France.

Firstly, Italy is a narrow peninsula with mountains in the center capped by the Alps at the top. The Allies needed to get about 70 American divisions into the fight, plus British and commonwealth forces and the French. There wasn't enough frontage, or front line space in Italy for this many troops, and there isn't enough road and rail connections to supply them.

Southern France is a bit easier, but the logistics do not compare favorably to Normandy. Normandy is within 100 miles of Britain, where the allies had the highest concentration of air power and the easiest place to stage large numbers of troops to. The closest spot to Southern France is Corsica, which is not logistically developed enough (ports, rails, etc) as a base for the massive allied air power and army staging. Northern France is also just far more convenient in terms of Air Power, and even Allied short range fighters could cover the Normandy beaches from Britain. Northern France was also more economical in terms of shipping, which always manages to pinch a military even when it has a huge amount.

Lastly, there is a strategic virtue in having multiple efforts. Spreading out the invasion points forces the Germans to spread out their defenses. The more spread out they are, the more that the campaign can result in mobile warfare instead of a static war of attrition. The Allies were always keen to avoid a trench warfare situation, and knew that only by forcing more mobile warfare could they chew up huge portions of the German army. This is pretty much what happened in August 1944, the German retreat out of France cost them casualties that even meant something in comparison to the casualties the Soviets were inflicting at the same time in the East.

Good answer. I agree with everything /u/white_light-king said and would like to add some extra context to an excellent response.

You say their South of France landing was virtually unopposed. This was because of everything that happened between D Day and Operation Dragoon. If Operation Dragoon had happened on the 6th of June 1944 the resulting German reaction would have been very different. I would also add that what white light king said Northern France was also more economical in terms of shipping can not be overstated. For me, this is THE most important point. I don't see how they could have realistically solved it if they landed in Southern France. Logistically, building up the bridgehead and pumping in resources, Northern France makes much more sense.

The other question arrives, why Normandy and not Brittany (west) or Pas-de-Calais (east)? As Brittany is a peninsula they wouldn't have the option of which direction to breakout and thus the Germans could seal off the landing much more easily. In Normandy the Germans had to make much more difficult decisions about where to deploy their resources as the British and Canadians could have breakout on the east while the British or Americans could have broken out in the centre/south and finally there was the breakout on the western part of the bridgehead, Operation Cobra. No one wanted to fight Germans on a bridgehead the size of the Brittany peninsula, you can only go east. Pas-de-Calais was heavily defended and also where the Germans expected the Allies to land, so while landing there would be better logistically in terms of supplies and distance to Berlin it didn't make sense in terms of force ratios and amount of defense.

Spreading out the invasion points forces the Germans to spread out their defenses was pretty much the British strategy for every major attack they launched from the 2nd battle of El Alamein onwards. It worked well in Normandy with the Germans throwing units in piecemeal as they arrived because of keeping many of their troops in Pas-de-Calais until it was too late.