It was absolutely more liberal than Russia or Austria -- or Spain, Prussia, Naples, or Savoy. There was more freedom of speech, more freedom of the press, clearer and stronger property rights, no serfdom or other feudal hangovers, and there were at least gestures in the direction of representative government and public participation in government. The Code Napoleon provided some degree of formal protection of these rights, including the rights of criminal accused -- due process, as we would say today. And while the Catholic Church got a "special position" after the Concordat with the Pope, there was full legal equality for Protestants and Jews.
Now, to be clear, Napoleonic France would not be considered very liberal today. It was a strong monarchy with most (not quite all) power vested in the sovereign. There was censorship -- "more freedom of the press than early 1800s Russia or Austria" is still a very low bar. There was a very strong secret police, and you could absolutely be arrested on suspicion and held for weeks or months; the Code Napoleon pretty much went out the window where national security was concerned, and national security was increasingly broadly interpreted as the Empire went on. You needed papers to travel around much. Assembly was okay but protest could easily get you in trouble or in jail.
Nevertheless, on balance Napoleonic France was a pretty liberal regime by the standards of the time. Maybe not the most liberal in Europe -- that would probably be Britain, though there were some odd little liberal states in the Holy Roman Empire, and Denmark was pretty okay after the Streunsee Reforms. But in the top two or three.
-- You'll occasionally see people claim that ancien regime France was also very liberal, maybe even as liberal as Napoleonic France. This is a weird argument that afaict was first advanced by monarchists and then got picked up by Catholic Integralists and spread around. It's... maybe one quarter true? France under Louis XVI was surprisingly liberal in some ways; there was de facto a lot of press freedom, for instance. But the nobility were legally superior to everybody, most peasants were still effectively bound to the land, the law code was a scrambled mess, the letters de cachet system gave the King huge powers to arrest and exile people (even if he didn't always dare use them), and you really wouldn't want to try openly practicing any religion but Catholicism.
Also, one huge difference that set Napoleonic France apart was the ideological underpinning of the state. It was said that other monarchies had subjects, while the Empire had citizens. And citizens had rights. Those rights might have limits, and they might often be ignored, but they were there. This was a radical change from the top-down mentality of most of Europe, where the great majority of citizens only had whatever rights the King and aristocracy granted them.
Was life for the average person better -- mostly yes, subject to the caveat that Napoleonic France was at war almost non-stop for 18 years, and wars don't generally make people's lives better. But most of France consisted of peasants, and the peasants suddenly got freedom from all those horrible medieval legal burdens. They got a law code that was easy to understand and that made sense. They no longer had to deal with the aristocracy -- the local lord in the big manor house? He'd either made peace with the Revolution, or fled.
And most of all, the peasants got land. Remember, the Revolution confiscated all the lands of the Church and most of the lands of the aristocracy, and either sold it at auction to support the assignat system, or distributed it to the peasants. True, some of it was returned to the Church under the Concordat, and a lot of it got purchased by speculators. But we're talking about a ridiculous amount of land here, and a fair chunk of it ended up in the hands of the peasantry. Before 1790, the modal Frenchman was a landless peasant. After 1800, the modal Frenchman was a peasant with land. This was a huge, huge change, and one that still shapes France today. Rural France literally looks the way it does because of what the Revolution and Napoleon did.
Most of the distribution happened before Napoleon took charge, sure. His key contribution was to confirm it, make it irreversible, and to introduce a legal code that made it pretty much permanent.
So just that one change -- the redistribution of land -- made a huge difference to the average French citizen.