The US, UK and France hit Syria. Will it work?

 The Al Assad family.  Snappy dressers and head of a murderous regime.  The current dictator is in the upper row, second from the left.

And by work, I guess, I mean will it deter Assad from gassing his people in the future?

I doubt it.

Assad is essentially a species of murderous fascist propped up by a tottering theocracy and an oligarchic corruptocracy.   But for Iran and and Russia, he'd still be struggling as the leader of one faction against a host of others. The others, for their part, vary from semi quasi democratic Kurds, Not Communist but you can see it from there Kurds, Socialist, and Islamist.  None of them, except perhaps the Kurds, can get along with each other and nobody can form a government that anyone else will tolerate.

Syria is a real mix. It's home to Sunnis, Shiia, Alawites, and Christians.  And its broken.  Ruled now by the Baathists, who are basically a regional fascist party, and by Alawites who are Baathist at that, it's a house of cards and hopelessly broken for the near and middle term.  Iran, for that matter, also is.

It can't be put back together.

Preventing further gassing would be nice.  And it has to be tried.  And the raids, therefore, had to be done.  But it's not going to work.

What would replace these folks (ignoring what we'd get in their place)?  It's hard to say. But with Iranian and Russian backing, they'll be staying in place.  Iran will take care of itself, as the Iranian regime is on the guillotine reading Archie cartoons.  Russia?  Much harder to say.