The map of 1815 France with all its departments (provinces):
All 4 armies managed to cross the borders into France in the same week.
The Austrians crossed the border and headed west to link up with the Spanish who had crossed the border and marched north east. Scouts were sent ahead and to the north to ensure a safe link up prior to any interference by the French.
The English had landed in Belgium and marched east to link up with the Russian army as it crossed into France. The conbined armies cross into Moselle only to be confronted by a French army already partly deployed in front of its route of march. This army had no option but to deploy and fight its way through the French defenders.
Click here for Campaign: 1815 Invasion of France - Part 3