Truly, who would need to choose alcohol as their poison at that time in France, it was the spirit of freedom and societal change that made one lose his or her head! Bad jokes aside, the choice of non-alcoholic psychoactive substances at this particular time in these partiular countries, was only barely starting to resemble the variety we mostly think of today. There certainly was no cocaine as someone suggested before, because it’d be only isolated in 1855, although I believe that the coca plant was known to physicians, thanks to the inclusion of it’s description in Institutiones Medicae of the Dutch physician Herman Boerhaave.

Opium was most certainly known of. At the very beginning of the 19th century, East India Company assumed control over the production of opium in Benghal and was transporting massive quantities of it to China, through ports like Macao (not declaring it, because Chinese officials were trying to put anti-opium laws in place). Back home in England, the tincture of opium (I know, I know, you said no alcohol, but it’s hard to avoid it) known as laudanum was widely available, however, the recreational use of it wasn’t a huge societal issue. Medical use of opiates as sedatives, cough suppressants and alike was on the rise and especially many soldiers soon got to know the effects of morphine, which was isolated from poppies in 1803, by a quite young Friedrich Sertürner. Throughout the century, many other plant alkaloids were isolated and put into medical (and other) use, based on Sertürner’s discovery.

As we mentioned soldiers, it is necessary to note that some cannabis was definitely used by the French. Just not much in France. Napoleon and his Armée d'Orient ventured into Egypt and Syria, where they soon got to know the local culture and importantly, vices. Chief among these, hashish. When the soldiers returned and brought the drug habits with them, it was then the role of the intellectual elite and the artists to further popularize these lovely poisons amongst the common folk. Certain monsieur Baudelaire was highly instrumental in this unfortunate business as well as making sure that absinthe will become the quintessential French alcoholic drink of the 19th century (I am including this as plenty of people will downplay the role of alcohol and demonize the part that thujone plays in psychoactive effects of absinthe. Pay no mind to them. Any evil done by the green fairy will be traced back to it’s relation to and inclusion of that treacherous molecule, ethyl alcohol)

OK, well, but I am in France or England, I’m not mingling with veterans or artists and I am not going to spoil my tongue by drinking booze. What do I choose? Why, of course I shall move into the completely opposite direction and allow my mind to be refreshed, not numbed! Caffeine should do the trick just fine. And even better, while my brain is pulsing with new energy, I might do some business as well. By this point coffee houses were very much established in England and even being somewhat replaced by tea rooms and tea houses. Cafés in France on the other hand will only rise in popularity and importance to society. Indeed, the societal divide you suggest was noticeable in the attendance of cafés by those who thought themselves an elite. Elite that would soon try to make sure to get rid of another type of elite. In July 1789, in Café du Foy, you can find Camille Desmoulins standing on the table (ah, the manners) and calling people to arms, which they would take up and storm the Bastille (and free all 7 of the prisoners). Ushering in a new age. And lots and lots of executions.

Monsieur Desmoulins’ cup was probably filled with liquid that was brewed with plant matter coming from Saint-Domingue, which we know today as Haiti. And that plant matter was grown and picked by a slave, who lived in horrible conditions. And who, two years later would too take up arms and alongside others would fight in a brutal revolution against the slavery and colonialism. Succesfully. Napoleon did shortly after, in 1806, try to make France the producer of goods such as sugar, that would not need pesky colonies to import them from. Coffee they did not manage, but they could grow chicory, which became a rather popular subsitute and additive into a coffee brew.

So, it would depend on your social circle, but truly popular really were coffee, tea and it would be hard to avoid alcohol if your goal was intoxication.

Some further reading:

Uncommon Grounds by Mark Pendergrast

Forces of Habit by David T. Courtwright

Opium: A History by Martin Booth

Cannabis: A History by Martin Booth

If you can get it, there’s a nice article to be found on JSTOR:

Coffee as a Social Drug by Steven Topik, in Cultural Critique No. 71, Drugs in Motion: Mind- and Body-Altering Substances in the World's Cultural Economy (Winter, 2009), pp. 81-106

(please, do not be mean to me about citation standards, I’m glad I can manage APA when I really really need to)

My credentials are "A person that reads books and stuff" so if I am inevitably schooled on all I got wrong, I'll be happy to learn more!