Very few Vichy members especially prominent ones were facist.
The ideology of the Vichy regime can be expressed in a few core beliefs.
The Third republic was a failure
ProGermanness/anglophobia - in a geopolitical sense
Anti communism
Much of this stems from what they saw as the failure of the French Third Republic 1870-1940. Often being unable to maintain a stable government and seeing the country experience huge losses in the First World War, and then weaken by strikes and poor leadership lose the Second.
They believed the French nation needed to b reborn. And surprisingly based their creation myth around the Battle of Alesia where Vercingetorix lost to the Romans. They argued that the defeat there had created a unified France. And that their defeat in 1940 would do the same.
However for this rebirth to be effective a purging of liberal and communists who weakened France was necessary which justified the Authoritarianism of the regime.
And thus Vichy is perhaps better seen as the pendulum swinging back to the French right instead of them being completely novel and new.