Galois didn't take part in the French revolution, he was born well after. On the other hand it is true that there was a lot of turmoil in French politics during his time, and that he was pretty radicalized himself.
He was involved in the July revolution of 1830, which overthrew Charles X and put Louis-Philippe on the throne (though Galois was a republican, and he did not do much). So he was part of a French Revolution, just not that of 1789.