Having taken a look at the reasons England had for not weighing in on the side of the Confederacy, we'll now continue with the second half of Rhett's line and examine France's stance:
"And as for France, that weak imitation of Napoleon is far too busy establishing the French in Mexico to be bothered with us. In fact he welcomes this war, because it keeps us too busy to run his troops out of Mexico..."
--Gone with the Wind, Chapter XIII
The "weak imitation of Napoleon" is of course Napoleon III, the nephew of The Napoleon (tm, because Bugsie likes him a great deal) and emperor of the Second French Empire. Now, weak imitation of his uncle or not, Napoleon III had plans for the world. All of the world, but some areas in particular. And it so happened that he had a most excellent plan with everything south of the United States, a plan known as the "Grand Scheme for the Americas." Don't let its name deceive you, the Grand Scheme was quite simple really. First step: France gains control of Central and South America and their resources. Second step: France rules the world.
Napoleon saw an opening for his first step when Mexico (temporarily) ceased to pay its debts to its European creditors in 1861. France quickly made an alliance with the other wronged parties, Spain and England, launched an attack on Mexico, lost its allies on the way (they caught wind of step two and didn't like it one bit, basically), but still managed to take control of the capital and install Maximilian of Hasburg at the head of a puppet state under French control. Most of this was accomplished because the United States had the courtesy to be otherwise engaged at the time, so yes, the French did welcome the American Civil War in this respect, as Rhett says. After the Civil War ended, the US troops and the Mexican resistance would in fact run them out of Mexico.
But just because the Civil War suited his purposes quite fine, that doesn't mean Napoleon III didn't have a favorite in this race. He was on the side of the Confederacy, mainly because he thought the Southerners would tolerate his presence in Mexico more easily. He was quoted saying that if the North won, he would be glad, but if the South did, he would be thrilled. ("Si le Nord est victorieux, j'en serai heureux, mais si le Sud l'emporte, j'en serai enchanté!") But despite this, he wouldn't act unwisely (for a certain value of "wisdom," where "wisdom" = "what would England do"). And England would not act, for reasons we discussed last week. So France didn't either. And the rest is, as they say, history.