France had a very effective internal police/intelligence system. In 1808, the revolutionary turned secret policeman Joseph Fouché is the Minister of Police. Foreigners are reported long before they get to Paris; Godechot characterizes the Napoleonic regime as "perhaps the precursor of the modern police states”. It won't be your "accent" that betrays you, it'll be whoever's ferried you across the Channel who has a chat with the harbormaster. Authorities on France's frontiers had the duty to know who was crossing the borders, to check passports, to relay information up the line.

We have immense volumes of Fouché's reports to Napoleon -- they're a little more frequent than weekly, but not quite daily. Fouché's many spies report on anything and everything that might signal domestic opposition, and foreigners are very much noted. Fouché tells Napoleon of his efforts to forestall British espionage as well as to maintain the Continental system's trade restrictions on the frontiers, for example at Anvers/Antwerp where the commissaire général de police, Jean-François de Bellemare has his responsibilities:

« Le ministère anglais a établi à Anvers le centre de la contrebande. C'est à cette ville qu'aboutit presque toute la correspondance relative à l'introduction des marchandises anglaises et, quelques fois, à des projets plus criminels encore [...]. Il est important d'établir sur ces points une surveillance proportionnée aux moyens que l'ennemi peut y trouver»

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"The English ministry has established a center of illegal activity at Anvers [Antwerp]. Its from this town that nearly all traffic relative to the introduction of English goods and sometimes, even more criminal plans occur. It's important to establish at these points surveillance posts proportional to the enemy's activities"

Not only does Fouché report, Napoleon frequently marks up these reports with questions and orders about particular individuals.

Here's Napoleon to Fouché from September 7, 1807

Give orders to have Mr. Kuhn, the American consul at Genoa, put under arrest, for wearing a Cross of Malta given him by the English, and as being an English agent. His papers will be seized, and an abstract of them made, and he will be kept in secret confinement until you have made your report to me. This man, having received a foreign decoration, ceases to be an American. I am sorry, by the way, you should have communicated with the ambassador of the United States. My police knows no ambassadors. I am master in my own house. If I suspect a man, I have him arrested. I would even have the ambassador of Austria arrested, if he was hatching anything against the state.

So you can abandon all your plans to "lie low" in France. It was a well organized police state. As an Englishman "on the run" you'd have much more luck finding yourself an out of the way spot in England, where the police were not nearly so ferocious. If you're feeling like rolling the dice, you might offer yourself as a spy to the French-- they were interested in foreign intelligence and if there's some reason that you can convince Napoleon's spies that you might be of use to them, you might be able to make a deal . . . but that's quite a roll of the dice. So, for example, the sometime political pundit and publisher Lewis Goldsmith is for a time very much in the service of Talleyrand, pumping out French propaganda in London, they clearly thought him useful for a while (though he then turns 180 degrees and denounces Napoleon and Talleyrand).

Further reading-- so far as I know pretty much everything is in French, but Lapham's Quarterly did do a very few selected translations, available here

If you can read French then there's a ton of material -- reading the volume of police reports gives a real feeling for how the Napoleonic regime worked, and how little it missed. They're the "Bulletins quotidiens adressés par Fouché à l'Empereur" -- many volumes, edited by d'Hauterive as La Police Secrète du Premier Empire

See:

Ernest d'Hauterive, "Napoleon et sa Police" (Paris:1943) -- interesting that d'Hauterive published this while France was occupied by the Nazis; I've often wondered whether there was a message there.

Renglet, Antoine. “Un Système Policier Impérial ? Le Commissaire Général Et La Police Municipale D'Anvers (1808-1814).” Crime, Histoire & Sociétés / Crime, History & Societies, vol. 20, no. 1, 2016, pp. 107–127.

Jacques GODECHOT, Les institutions de la France sous la Révolution et l’Empire: Vendôme: Presses Universitaires de France, 1989

Isser WOLOCH, Napoleon and his collaborators: the making of a dictatorship, New York: London: Norton & Comp., 2001,