If you look below the map on the back of a euro note, you will notice three small boxes. The shapes inside them mark overseas territories that also use the euro, and the one on the left is French Guiana. Although it looks tiny on the map, it is in fact the size of Portugal, and is a fascinating relic of colonialism: an outpost of Europe in South America.

Bordering Brazil and Suriname, French Guiana doesn't just belong to France – it's part of France. People are paid in euros, have French number plates, speak French, and the biggest employer is the French state. The French flag flies above the town hall of Saul, a village in the Amazon rainforest. Ninety percent of what the country consumes is imported from France, which makes things absurdly expensive – but available if you have the money. A pack of 10 strawberries will set you back €9 ($12).

The one thing that is cheap is rum, at €4 a litre, and the signature drink is ti ponch – rum with sugar cane syrup and lime. In the evenings, informal Surinamese restaurants serve bami and nasi, Indonesian satay dishes brought by the Dutch, or pieces of shark meat on skewers. During the day it's common to see men carrying birdcages, exposing their picolettes to as much sunlight as possible.

The population of French Guiana is only 250,000, but it has an amazing mix of ethnicities. It has the highest standard of living in Latin America, and this attracts migrants from Brazil, Suriname, Haiti, Guadeloupe and Martinique. Virtually all of the supermarkets are run by a Chinese minority, and most of the fruit and vegetables are produced by a community of Hmongs who were forced to flee their native Laos. Then there are indigenous people, whose way of life hasn't changed for centuries.

Both banks of the Maroni river are identical – trees as far as the eye can see. However, one side is part of Europe and the other is Latin America. You would think that this would therefore be a heavily patrolled border. Not so: as your boat approaches the French side (there is no bridge), the boatman asks whether you would like to go through customs. If you don't, he will simply drop you off a bit further downstream. If you do, you are likely to find the sleepy border post closed. It is a strange welcome to Europe.

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