They are two factors to take into considerations. The first is that Vichy wasn't really united in purpose, many of the higher up of the régime had different views on what course of action to take, forming several factions within the régime with competing goals and views. Many were completly on board with fascism and collaboration and pushed for a counter-attack against the Allies because of ideological reasons and because they believed in Hitler's vision for Europe. Some were extremely nationalists aswell but in a more pragmatic way, they had no love for the Germans and were very much aware of the precarity of their situation and they tried to use their potential entry in the war to gain concessions from Germany. And some even had pro allies tendencies, and simply didn't want to fight them at all. For example general De Lattre de Tassigny who disobeyed orders from Pétain to simply let the German invade the free zone in 1942 and tried to mount a defense, only to be condemned by his superiors and as a result defected to Free France.

The second is that the terms of the 1940 armistice weren't definitive, Hitler wanted to wait to have both France and the UK having asked for peace before making a permanent settlement. So during the entire war there is this sword of Damocles above Vichy's head of what is exactly Hitler's plan. Will he simply ask for a return of Alsace-Lorraine ? Will he ask of more ? What about Italy and it's claims on places like Savoy or Corsica ? What about the empire ?

Both of this elements lead to a situation where the Vichy leadership is quite frankly paralysed, it doesn't know what are the Germans plans so it's impossible to know if joining them would even be worth it, and the leadership is also blocked by it's own internal divisions. The most pro nazis want to join the war simply because of ideological reasons, others are trying to negociate their help for concessions on things like the allowed size of their army or garantees for the French colonies. As I said many Vichy officials are very much far right and ultra nationalists, but they also have no love for the Germans and aren't going to join their war for nothing. And finally some are even working against Germany, the Vichy army conducting secret developpements of weapons forbidden by the armistice, like for example the ARL 44, a heavy tank, or preparing large camouflaged weapons cache in preparation of a rapid expansion of the army if needed. Some in the High Command even prepared a plan to join the Allies in case Hitler tried to invade the free zone by letting the anglo-american seize the port of La Rochelle, although this proposal will be quickly shot down.