The Vichy French fought the allies in Africa, Syria, and even Madagascar. Considering how explosive anti-Nazi sentiment was after their liberation (rape and humiliation of Nazi sympathizers), it blows my mind how the puppet government could find troops to essentially fight FOR their historical rivals that had just destroyed their country.
Did they have problems maintaining discipline? Was desertion a serious issue?
EDIT: I realize similar questions have been asked before. To emphasize distinction. This thread concerns the legal impacts of Vichy France. This one wasn't really answered.
The Vichy French Army is not at all the same as the French Army in 1940. France used a conscript army, and most of the soldiers were either stuck in German POW camps or went home after the armistice. After the surrender, and just like Germany after the Treaty of Versailles, France was allowed to keep a small army after the armistice in 1940, a small metropolitan defense force of around 100,000 (in all branches) for keeping order in France. This was the Army of the Armistice. Saying that they fought for the Germans is not true - the French government still existed, and still maintained its independence, even though Germany was looting half of the country and could force the other half to stay in line. So in short, they didn't need to find any soldiers, as the army was radically downsized.
This surrender of France was a complicated affair, and it will suffice to say here that many French citizens believed that Petain meant to fight on at a later date. Furthermore, professional soldiers, then as now, tend to lean towards the right politically, and may have sympathized to some extent with the Vichy regime, which was reactionary. And anti-British sentiment was rife after Mers-el-Kebir, the British attack on the French fleet in North Africa. The French Army in North Africa did not really deal with any German or Italian interference, isolated from metropolitan France, but they still regarded the government in Vichy as the legitimate government, and the Free French as renegades, which, essentially, they were. It must be remembered that, no matter how odious the Nazis were, Petain's government was the de facto government of France. However many officers of the French African forces detested the Germans, like you imagined, and conspired for the time when they could have a rematch, an opportunity they received when the British and Americans invaded North Africa during Operation Torch.
On the topic of maintaining discipline in the Vichy Army, soldiers did in fact smuggle a lot of weapons and equipment into the countryside, for use against the Germans if the chance ever came. Other Vichy authorities turned a blind eye towards clandestine resistance, and many of the French resistance's most important groups were located in Vichy territory in the south.
This is a bit of a sloppy answer but I'm happy to answer any follow-up questions or clarify my answer if you'd like.