For Libya, mostly by giving fake intel to the UN (and by extension to the US), George W Bush 'WMD' style (though it was a bit more compelling). I'm not knowledgeable enough to know if the UK was aware of it or if the Mi6/SIS was fooled.

For Syria, Obama made threats to try to prevent the use of chemical weapons. The UK wanted to avoid another Libya, the other EU countries aren't warmongers, Turkey wouldn't have said anything, so only France did the 'actually, they used chemical weapons, and the US is not alone if you go so you won't have another Iraq!'.

I don't know what happened to Hollande, why he grew a pair suddenly, but I don't think we ever had a president who didn't stir shit at least once in 70 years.