There are different ways to named the country of France. Some of the examples describe sometimes just a part of France and not all of the territory. Most of those nicknames come from the long history of France.

1 – La France
This is the most common way to named this country. The name comes from the 5th century, different Frankish kingdoms succeed to the Roman occupation of Gaul. These kingdoms are spread over part of northern France, Belgium, the Netherlands and Germany. The name “France” comes from the word “Franc”.
The Frankish people are a people of warriors who elect their leader, the king of the Franks. They freely decide to go to war with him. This is why the word “Frank” also meant “free man”.

2 – La République française or La République
Another way to call the country of France, “The Republic”. This come from after the creation of the first republic of France in 1792 after the French revolution in 1789.

3 – L’Hexagone
This nickname refer to to the shape of France of hexagon. We can see a six-sided polygon. There are three land sides and three maritime sides. This is why the expression Hexagon is frequently used to describe the French territory.

4 – Le pays des droits de l’Homme
This nickname “The country of human rights” is the result here again of the French revolution in 1789 with the creation of the Declaration of the Rights of Man and the Citizen, a central text of the French Revolution.

5 – La Gaule
The Gaul was a time, more than two thousand years ago, where the borders where close to the ones of the actual France. This a humorous way to name France and to refer to his history. This part of history gave to France his national animal symbol: The rooster. This animal never give up and fight until the end. For example, you can see the animal on the national jersey of the Football, rugby and handball teams.

6 – La France métropolitaine or La Métropole
The “metropolis”, is the way, in the international law, to call the French territory in Europe. This include the island of Corsica. By the way, I wrote an article about traveling in Corsica: Corsica: The French Road Trip Island

7 – La France continentale
“Continental France”, another way to describe the French territory located in Europe.

8 – DROM-COM or DOM-TOM or La France d’outre mer

With the reform of the regions (=states) set up on 1 January 2016, the Overseas Departments / les Départements d’Outre-Mer (DOM) and Overseas Territories / Territoires d’Outre-Mer (TOM) have disappeared. The term “DOM-TOM” does not exist anymore but the French people still use it. The new name is DROM-COM.

5 Department and Overseas Region / 5 Département et Région d’Outre-Mer (DROM): DROM is now use for the former DOM
Guadeloupe, Martinique, French Guiana, Reunion and Mayotte.

5 Overseas Communities / 5 Collectivités d’Outre-Mer (COM):
Saint-Barthélémy, Saint-Martin, Saint-Pierre-et-Miquelon, French Polynesia, Wallis and Futuna

Exceptions

1 Oversea Communitie (COM) with a special statut:
New Caledonia

3 Overseas Territories / Territoires d’Outre Mer (TOM):
The acronyme still exist for those territories
French southern lands, Antarctic Lands and Island of Clipperton

DROM-COM source wikipedia

Countryside nicknames for France

9 – La province
This is a word that I and non parisians french people hate a lot. I hear only this word when I meet parisian people. The province is everything except Paris. Being from the north or south or anywhere is exactly the same for them. It sounds really arrogant when a parisian use it.

“Ah, t’es de la province ?”

(= Ah, you are from the province?”)

10 – La France profonde
The deep France is to describe the parts of France disconnected from the big French cities.

Bonus: La diagonal du vide
The empty diagonal is a huge area where the population is quite low. It goes from north-east to south-west of France. The “diagonale du vide” is la France profonde :p

This is it for the article. Now, I invite you to read more article about 3 Original activities to do in Lyon

Credits:
https://www.boeser-wolf.schule.de/allemagne/france-allemagne/langage/pourquoi-la-france-s-appelle-la-france.html
http://www.outre-mer.gouv.fr/les-territoires
https://www.legifrance.gouv.fr/affichTexte.do?cidTexte=LEGITEXT000006068137&dateTexte=20190226