Well, for the army. Naval semaphore (flags) could pass information across serious distance. Scout ships would often be over the horizon from flagships, their messages relayed back in minutes. The speed of pre-electric mechanical communication is underappreciated today.
Also, carrier pigeons were faster than horses.
"Messenger pigeons were used as early as 1150 in Baghdad[8] and also later by Genghis Khan. By 1167 a regular service between Baghdad and Syria had been established by Sultan Nur ad-Din.[9]"
Still useful only between (or at least to) given established points, and adding new nodes took time.
Consider that a critical advantage of the Germans over the French in Fall Rot, June, 1940, was radio-equipped tanks, enabling direct unit-to-unit comms and improvisation on the battlefield.
Still, it's sobering that the Royal Road represented the plateau in long-distance information transmission for very nearly 2500 years:
https://en.wikipedia.org/wiki/Royal_Road
I'll also highlight the key phrase tended to be in my original comment.
- Use was all but entirely limited to France. On campaign, mesages would revert to horseback.
- It was stopped by inclement weather.
- Net throughput was low, though I don't have a source on message traffic.
- Messages would have been brief ... one might say telegraphic. Little detail could be conveyed.
- Access was limited to government business. At least some of Napoleon's correspondents were likely denied access.
As counsel to others, Napoleon's mail-handling protocol would be subject to the long transits I describe.