Except that your QRH will probably say to cut off or not deploy pax O2 supply in case of smoke in the cabin, it's at the start of the list for my type. That is to restrict any excess O2 that the fire could use to intensify, any fire within the cabin is a real emergency as there is limited ability to fight it, smoke and fumes builds up rapidly, there is usually an emergency ventilation procedure you can use once the fire is extinguished. There have been cases where a smoldering fire has raged when the exits were opened as it introduced more O2 from outside air. Remember the cabin crew only have a couple of BCFs or such for less than 1 minute of fire fighting, you don't want any excess fuel or O2 added no matter how small the amount. Engine failure/fire should be limited smoke, I've had fumes in the cabin from various engine related problems from electrical to oil vapor, it's nasty and shutting off the source or bleed will stop it pretty fast.
FAs have some portable oxygen for those that are struggling.
Probably good to remember that a few lung issues is better than the fire spreading and the aircraft being lost. Once on the ground Evac ASAP if it's that bad.
I think some form of smoke hood/mask should be carried on airliners similar to life jackets. Even if it just provides some filter and no O2 it's better than nothing.