Short answer:
Nope. Much was promised, but you didn't cross Napoleon.
Discussion:
Napoleon was a keen and ferocious observer of the press, and indeed of popular literature and the theatre. He was even kept informed of what people said about him in bars, in Police Minister Fouché's Daily Bulletin. While there are significant differences in talents and powers, in their inclinations you can see a resemblance between Napoleon and intolerant contemporary political figures. The existence of republican forms and freethinking aspirations does not preclude the rise of despots, but it does shape the language they use.
Rights were often promised under Napoleon -- sometimes to compare with Britain, which had a notably free press-- sometimes as part of the Revolutionary tradition; rights which couldn't be exercised in practice. "Freedom of the Press" under Napoleon bears some a parallel to the freedom of the press "guaranteed" under Stalin's 1936 Constitution.
In a letter to Fouché, he says:
[M]a volonté est que la censure n'existe pas, j'ai lieu d'être surpris de voir, dans mon empire, des formes qui peuvent être bonnes à Vienne et a Berlin. S'il existe sur cela un usage que je ne connais point, faites m'en un rapport. J'ai longtemps calculé et veillé pour maintenir la liberté politique. Je n'entends pas que les Français deviennent des serfs.
[trans]
My will is that censorship not exist, I have occasion to be surprised to see, in my Empire, things which might go in Vienna and Berlin. [EG, in this letter of 1806, there's still a "revolutionary" idealism; he's contrasting what he wants for his Empire with the antique reaction of the German monarchies]. If this is going on here and I don't know about it, report it to me. I've long calculated and maintained watch to maintain political liberty. The French [will not] become serfs.
That all sounds great, a siècle des lumières enlightenment spirit . . . er . . . not so much.
Napoleon was frequently provoked to fury by articles or indeed theatre pieces of which he disapproved, and his response was often that they should not be permitted to be printed, or if already printed, should be seized and destroyed, and their author punished.
So we frequently find Napoleon, annoyed by something he's read, writing to Fouché with instructions like
Il est tout à fait indécent que des hommes si ignorants écrivent d'une manière classique sur des choses qui se sont passées de nos jours. Faites supprimer ce volume
[trans]
It is completely indecent that such ignorant men write old fashioned [nonsense] on today's affairs. Have this book suppressed ["suppressed" meant banned from publication, copies seized]
Similarly, just after the Coup Brumaire, Napoleon remarks
Si je lâche la bride à la presse, je ne resterai pas trois mois au pouvoir
[trans]
If I let up on the press, I won't last three months in power
How do we reconcile the ostensible respect for "freedom of the press" with these orders?
As with some of the 20th century dictators, Napoleon comes to power on an Enlightenment ideology, and he continues to adhere it as a matter of rhetoric, even as his tyranny grows. The Nazis, abjuring the Enlightenment, are intellectually the clearest about clarifying the seeming paradox, with their constitutional notion of the "Fuhrerprinzip", under which the leader's will is itself the highest expression of the law.
Napoleon and his 20th century counterparts weren't claiming the same kind of absolute monarchy as Louis XIV; as products of revolutionary traditions, they distance themselves from the antique -- note Napoleon's snide dismissal of someone writing d'une manière classique.
Historians don't tend to pay a lot of attention to the political rhetoric of dictators, beyond the machiavellian Kremlinology-- looking at language as codewords for "who's in and who's out". But despotism has its own rhetorical logics, and to understand Napoleon and his regime we have to grapple with the paradox of a despotism that emerges from Enlightenment values, and that has an ideological stake in them, even when in practical terms the Emperor has no tolerance for the exercise of the rights ostensibly guaranteed.
Sources:
D'Hauterive, Ernest. “NAPOLÉON ET LA CENSURE.” Revue Des Deux Mondes (1829-1971), vol. 61, no. 3, 1941, pp. 362–377.
D'Hauterive, Ernest. “NAPOLÉON ET LA PRESSE.” Revue Des Deux Mondes (1829-1971), vol. 55, no. 1, 1940, pp. 111–134.
Bourdin, Philippe. “Les Limites D'un Impérialisme Culturel : Le Théâtre Français Dans L'Europe De Napoléon.” Le Mouvement Social, no. 253, 2015, pp. 89–112.
GRANATA, Veronica. “MARCHÉ DU LIVRE, CENSURE ET LITTÉRATURE CLANDESTINE DANS LA FRANCE DE L'ÉPOQUE NAPOLÉONIENNE: LES ANNÉES 1810-1814.” Annales Historiques De La Révolution Française, no. 343, 2006, pp. 123–145.
Dobrin, Samuel. “The New Soviet Constitution.” Transactions of the Grotius Society, vol. 22, 1936, pp. 99–116.
Schmid, Ulrich. “Constitution and Narrative: Peculiarities of Rhetoric and Genre in the Foundational Laws of the USSR and the Russian Federation.” Studies in East European Thought, vol. 62, no. 3/4, 2010, pp. 431–451.
Pauley, Bruce F. “Fascism and the Führerprinzip: The Austrian Example.” Central European History, vol. 12, no. 3, 1979, pp. 272–296.