Matteo,
Austria was not a faithful ally. It was a defeated foe, and was only cooperative with France when it had no other choice, and backstabbed at the earliest opportunity.
The faithful ally was Spain, who willingly became an ally (albeit after a loss in the Pyrenees showed them who was the predominant military power. But still, was one of the earliest and the most faithful of allies). That worked out well for them.
This is what Metternich wanted everybody to believe when Nappy was defeated. But reality was different. Before the russian disaster, Austria bet on what everyone deemed certain : a lasting french domination.