The word you're looking for is 'Gendarme'.
A building starting with G is the Guggenheim in New York City.
A song starting with the letter G is Van Morrison's 'Gloria!'.
A musical instrument starting with the letter g is a guitar.
Gorila
An alcoholic beverage starting with G is gin.
Yes, a "gendarme" is a police officer in France who is part of a military branch responsible for policing in rural areas and small towns. They have both civilian and military duties.
This dance is called a "gavotte".
policier
a French policeman is 'un policier' or 'un agent [de police]'. The variety you find in rural areas are often 'gendarmes'
policeman
The "French" Policeman.
There is no such word as "genderman" in French. However, a "gendarme" is a policeman of military status working by the French countryside.
A mood starting with G is generous.
An attitude starting with G is gracious.
A gendarme is a policeman or constable. A gendarmerie is a police station.
A thing starting with G is garage.
A place starting with G is Genoa, Italy.