How did Allies secure southern flank during "Race to the Rhine"?

As the other answer mentionned, the Dragoon operation was a good way to cover the southern flank.

But other factors counted for the Allied fast run to the Rhine:

• First, the air power: it was not enough to pin down German retreating forces, but it was a good way to stop counter offensive (I do mean counter offensive and not counter attack)
• Second, the long battle in Normandy had forced the Germans to engage most of their forces available on the Western front (Italy, South of France and Norway excepted). Thus, when Allied forces encircle the Germans in Falaise, they had broken lots of German soldiers and they had broken through all their lines of defense. The Germans had not enough reserves to launch counterattack, because South West of France was nearly empty of troops (only 1 armoured division and 1 infantry division (French Combat Command 1) were chasing for them) and South East troops were attacked by Dragoon operation.
• Third, a very important point about the Dragoon operation: When the Allied successfully landed and defeated the German forces on the coast, the 19th German Army started to retreat. It was not a threat to Overlord because forces from Normandy, especially the French 2nd Armoured Division, was about to cut them off their rears. In the meantime, American and French forces from Dragoon operation tried hard to cut them in their retreat, but they eventually failed. You see with those points that 19th Army was less a threat to Overlord south flank than it was threatened by Overlord and Dragoon operations.

To conclude, during the Race to the Rhine, the Allies had little threat to their South Flank. Arriving on the Rhine, they met forces from the South (Dragoon).

One of the great tactical lessons of WWII, first learned by German generals, is that even a strong army is relatively easy to defeat and relatively incapable of significant fighting if cut from its logistical support. Once they were so cut from logistical support by the redeployment of German forces following Overlord, and especially after the junction of Dragoon and Overlord in mid-September 1944, the remaining western German forces paused no real danger to the allied forces. I add this answer only to promote the following link

http://www.youtube.com/watch?v=WOVEy1tC7nk#t=388

which is a great visual tool to understand the effectiveness of encircling enemy forces. In fact, the only position that survived encircling for a significant span of time was the German position in Stalingrad, and we all know why and how this ended.

To better answer this question you need to go back to the opening stages of the invasion.

Operation Overlord, the Allied invasion of Northern France took place beginning on June 6th 1944. However, it took several weeks for the Allied forces to break out from their initial positions and by the time this happened most of the German forces that had been in France were already deployed against the Allies.

Indeed, most of the German forces from the Channel coast including around Calais had already been deployed West to help in the defence.

Operation Cobra, launched on July 25th signified the start of the main breakout, this animation shows it quite nicely:

http://www.bbc.co.uk/history/interactive/animations/wwtwo_map_overlord/index_embed.shtml

So, up until this date the Allies were not concerned about any German forces in central or southern France - indeed by this time most German forces had been redeployed against the Allied invasion force.

You also need to bear in mind that operation Anvil (or Dragoon if you prefer) started on 15th August 1944 and this tied down what mobile forces the Germans did have remaining in Southern France.

More info about that less well known operation:

http://operationdragoon.org/

The Allies realised that any advance into Germany from France would be quicker and more effective if they advanced in a relatively narrow front rather than trying to clear the whole of France in one go and then advance on a broader front. OF course Paris was liberated as this was a strong signal that the German cause was doomed and a great boost for morale and the propaganda was useful.

A narrower advance along the coastal strip, through the Low Countries, largely bypassing the Maginot/Siegfried lines was easier to supply and would advance more quickly. Making the advance on a wider front through central France would lead the possible war of attrition along the lines of the First World War and the Allies wanted to avoid that.

With regards to the German strongholds you mention that held out until much later on, these were of little strategic significance and it was felt not worth the loss of life it would take to capture places like La Rochelle, so the allies simply surrounded them and waited.

The forces that were holed up in these fortress cities were not generally considered much of a threat offensively being more of an immobile defense force and by surrounding them they were nullified.