Question: In a world without fossil fuels, would air travel ever really be developed?

Without fossil fuels, the most likely path that could lead to the development of a proper industrial revolution would eventually be nuclear power and renewables. This world would probably start with hydro-electric power, in which they then move on to nuclear as scientists living in the cities that build up around dams are able to discover more about nuclear physics that would allow this to be harnessed as a fuel source.

While there are other questions that could be raised, how would air travel be developed in this sort of world? Could airships remain viable in the face of electrified railroads and nuclear transport across oceans?

Would fixed wing aircraft or helicopters eventually be developed? What fuel sources might they use?

Answer: 
***Lighter than air craft:***

While the modern combustion-powered aircraft would be a hard sell, there were [steam-powered airships](https://www.space.com/16623-first-powered-airship.html#:%7E:text=Henri%20Giffard%27s%20steam%2Dpowered%20airship%20flew%20in%201852.&text=In%201784%2C%20General%20Jean%20Baptiste,Meusnier%27s%20design%20was%20never%20built.) built long before the Wright brothers, and hand-cranked *designs* existed before that. After that, electrically-powered airships were constructed like the [*La France*](https://en.wikipedia.org/wiki/La_France_(airship)).

A steam powered model could certainly have been operational, utilizing charcoal or distilled volatiles, and in fact such designs predated ones using fossil fuels. Only the relative efficiency of fossil fuels caused them to predominate. In fact, the [diesel engines](https://en.wikipedia.org/wiki/Diesel_engine) invented by Rudolf Diesel initially ran on coal dust (easily a sub with charcoal) or vegetable oil, demonstrating that biofuels were already viable early in the history of aircraft. [Diesel aircraft engines](https://en.wikipedia.org/wiki/Aircraft_diesel_engine) were viable at the beginning of the aviation industry and are currently enjoying a resurgence.

Once the value and efficacy of aircraft were established, I doubt they would have simply disappeared. It is speculation to say if fixed-wing aircraft and helicopters would have been invented, but I'm guessing that as the manufacture of biofuels for various powered vehicles became more common, they probably would have been at LEAST invented, even if they didn't end up being practical. The versatility of these vehicles would probably still have led to at least specialized functions for them.

But I'm confident there still would have been blimps and dirigibles, and likely better ones than we have today due to lack of competition from gas-guzzling fixed-wing craft. Land and sea transportation also benefited from fossil fuels, so weaker competition in these arenas means the airship would have been quite reasonably competitive as a passenger and even cargo transport.

You may find [this](https://worldbuilding.stackexchange.com/questions/67461/realistic-airships) question relevant to your question.
River-side mill towns existed before electricity could be used to export energy.

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> Would fixed wing aircraft or helicopters eventually be developed? What fuel sources might they use?
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sailplanes, definately.

Oowered craft, maybe for military applications, and use by the very rich. They would probably be ethanol fueled, it's hard to speculate on which type of engine they would use.