The direct grievances between France and the Austrian Empire came from the Vienna System. In the previous great wars, whether the Luxembourg Crisis or the Alsace-Lorraine Crisis, France's declarations of war on Austria had all stemmed from the Vienna System's constraints upon France.
Only now, two more aims had to be added: restoring national confidence and recovering lost territory. Though France and the Austrian Empire did not share a border, both were regional powers, and the contradictions and interests between them could not be reconciled.
And which side Spain fell toward would influence the future situation of both nations, and even of Europe. Therefore, as long as the Austrian Empire could be defeated in Spain, any price France paid would be worth it.
Not to mention that Spain was now the only country on the European continent with the same system as France. No matter what angle one looked at it from, France had no reason not to enter the war.
In the eyes of the French Republicans, an alliance with Britain brought a hundred benefits and not a single harm. After all, the French navy had suffered a grievous loss of vitality due to the Grand Orient Fleet's defection, and to truly expect a fleet cobbled together at the last minute from bits and pieces to risk its life against the Austrian navy was nothing but a fool's dream.
The Austrian Empire's supplies for its army in Spain were maintained entirely by sea transport. As long as the Austrians' maritime routes were cut off, there would be no suspense left in the outcome of the war.
In addition, by allying with Britain and fighting in Spain, France held the advantage of terrain. France could incite Catalonia to independence, then incorporate it into its own territory, while the British did