I’m especially interested in Louis Antoine de Bougainville’s voyage around the world in which there were two ships. It seems from my reading as if officers could exchange messages and even move between the different vessels, but sources don’t mention how. Could people on one ship have alerted those on the other to an emergency on board or the need for an urgent meeting?
In the Royal Navy and surely in the French, communication via flags was a long established procedure. That’s why the commander’s ship is called the “flagship”.
Before setting sail, all the ships of the fleet would coordinate the code book of flag to message. It would be pretty detailed. One flag would represent a concept.
Come within Hail may have been “a flag checkered red and blue at the mizzen” and each ship in the fleet would have their own pennant so this order could be directed as desired.
Other flags: Strange sail sighted, how many, in what direction, who are they Make more sail Anchor Land sighted
One could send a faster boat out to windward to check for enemies, weather etc.
Someone on deck or up the mast was tasked with paying attention to the flags on the command ship. In a larger fleet, ships would echo the flagship communications to others further away.
If the communication was urgent, the flag would be accompanied by a gun to get everyone’s attention.
One source: Naval Records Society Vol XXXV. Signals and Instructions 1776-1794
https://books.google.com/books/about/Signals_and_Instructions_1776_1794.html?id=gj8JAAAAIAAJ