Well, to put it bluntly, because it wasn't a civil war, it was a revolution. There were periods where certain violent revolts had cropped up against the central government (i.e. the Vendée uprising, the 'federalist' revolt that was never a single, unified revolt). These events are characterized as 'revolts' or 'uprisings' because they were never large-scale forces fighting, they were pockets of localized resistance that never had a unified group to other parts of France.

Now the so-called 'federalists' (i.e. those who wished to de-centralize power away from Paris, opposite of how the word is used in the United States) did try to raise an army of 80,000 men to march on Paris and dislodge the government. Now they never came anywhere close to getting that many men, and even those they did get were unwilling to leave their own region. However for the sake of your question: if the federalists had been able to unify 80,000 men under the same banner fighting for the same cause to wage war on the central government? I think we could possibly entertain the idea that a civil war could have come out of that. But since it's a counter-factual we'll leave it there.

On the other side, let's talk about why the French Revolution was a revolution. In the most cut & dry definition of the word, a revolution is a sudden and dramatic upheaval in the current order. France's revolution was THE revolution in this sense. The revolutionaries famously didn't limit themselves to the political question, and in less than 24 months had entirely reworked nearly every aspect of French life-- no joke. The judiciary, the physical boundaries, the taxation system, the government, the guild system, the church, the composition of lands, the currency... it'd be harder to identify something they didn't touch. I think the French more than meet the criteria for a revolution here.

Please let me know if you had any follow up or clarification questions!