Assumedly, the price of air travel would go up, making it only available to to the middle class and above?
However, come to think of it, one might want to give everyone some carbon credit or travel points, and then develop a market in it. (That would still mean that the rich will fly as much as they want, but at least they'll pay the poor that don't travel for the privilege.)
One of them is a pure carbon tax on all carbon emitting sources, which is regressive: it will affect poorer people more while affluent people can just conveniently pay more to emit the CO2 they need.
The other way is by specifically increasing taxes on income and wealth and using that money to invest in decarbonisation - for the most part by making solar, wind (and in some cases nuclear) cheaper, which eventually makes carbon more expensive in relative terms.
Governments these days tend to focus on the second way, either because it's progressive and therefore perceived as fairer, or because they see the alternative as political suicide (Macron's Gillet Jaunes appeared because of a proposed carbon tax on petrol)
This already exists, but the problem is that carbon credits are nearly impossible to regulate (it's very hard to prove that some carbon-reducing initiative isn't counted toward two distinct carbon credit programs or that the carbon is even reduced as promised). It's hard to do the accounting correctly for honest participants, which pretty much guarantees fraud among less honest participants.
The lower class is more susceptible to the effects of worsening air pollution and climate change. They see the greatest benefits in those categories as each are improved by a carbon tax.
The downsides for the lower class can be further ameliorated by making the tax redistributive, e.g. increased welfare benefits, lowering other taxes, UBI, etc.
That’s significant, but a ticket already generally costs $387 to $400/pp in moderate travel months if you take a bag.