I was always told that France was neutral once the Vichy Regime was set up after the Fall of France - that they were no longer in the war. But how could this be true if the Allies invaded French West Africa? Isn't this basically a declaration of war on Vichy France?
As well as this, once the Germans occupied Vichy France in 1942 after Operation Torch, was there fighting again between the French and the Germans or did they just surrender?
Vichy France did not officially declare war on the Allies, it was recognised as a neutral country although it did engage in fighting with both Axis and Allied forces throughout its existence (this is referred to as "armed neutrality").
Vichy France had a complicated relationship with the Allies, the UK in particular. As shortly after its formation the Royal Navy attacked a French naval contingent which at this time was based in French Algeria. The UK did this due to their fear that the French fleet would be used by the Germans against the Royal Navy. It resulted in Vichy France severing all diplomatic ties with the UK. Before they joined the war both the US and USSR recognised the Vichy French government.
As you mention there was also fighting in the French colonies, the Free French Forces had maintained control of some of the African colonies and used these as a base from which to launch attacks on the Vichy French colonies. There were also similar divided loyalties and conflicts in France's Asian colonies and the Japanese occupied French Indochina. The Allies had come to recognise the Free French as the legitimate French government after the Vichy French made it clear they would not join the Allies, so they were supporting the Free French Forces in their fight to reclaim territory which brought them into conflict the the Vichy French, specifically during Operation Torch although this fighting did not last long and most of the Vichy French forces in North Africa went over to the Free French.
When the Germans (and Italians) occupied Vichy French territory there was very little resistance by the existing Vichy army, they did not really have the military capabilities to fight the German army. Their only real act of defiance was scuttling their navy which denied its use by the Germans, as well as the Free French.
So to answer your question, Vichy France was in a state of armed neutrality towards both the Axis and Allies.
They fought each other in Operation Exporter, or the Syria-Lebanon Campaign. Virtually entirely Vichy French forces fighting against British, Commonwealth, and Free French forces. It was a weird campaign.