I know that "The Second Empire" used the American preoccupation in its civil war as a handy excuse to bypass the diplomatic barrier to the Americas erected by Monroe and involve itself in Mexico (Viva Mexico) and was contracted by the Confederacy to construct at least one ironclad ship (which interestingly enough found it's way to Japan and served as the "Kotetsu" in the Boshin War of 1868-69) but other than these attempts to profit indirectly from the war, (as any good neutral would do, an American tradition as well) was there any contemplation in the court of Napoleon III of taking a side more directly? were there embargoes on the Union, for example or was, for example the construction of the "Sphinx"/"Kotetsu" a private enterprise the government did not concern it's self with? And what of the opinion's of the French People? What did they think of the war for Liberte, and Egalite fought over by by Freres?
I can't speak to the larger French public, but the Confederacy definitely had sympathizers in France and Napoleon III was counted among their number. When the Confederacy reached out to France for diplomatic recognition, Napoleon supported the idea but refused to act independently of Britain. There were various attempts to produce a joint Anglo-French recognition of the Confederacy, but when Britain rejected these measures in June of 1863 the French decided to await additional Confederate successes on the battlefield. (Lee's defeat at Gettysburg a few weeks later would mostly put an end to this optimism).
Source: McPherson, Battle Cry of Freedom.