The British Channel Islands  are located just off the coast of France mainly in the Bay of St Malo but are not part of either. Formally they are Crown Dependencies, and are self-governing in all respects except for Defence and Foreign Affairs.
The Islands fall into two separate Bailiwicks (historic feudal divisions), each of which has its own separate government. Guernsey, Alderney and Sark (comprising the Bailiwick of Guernsey) is effectively a Customs Union with no customs controls between them (despite the fact that Sark levies taxes on alcohol and tobacco at a much reduced rate to the rest of the Bailiwick!)
Bailiwick of Jersey
Bailiwick of Guernsey
The larger islands are divided into Parishes. (Alderney is one parish, the Parish of St Anne).
The Channel Islands have been inhabited for over 5,000 years and have a long and colourful history. During WWII they were the only part of the British Isles to be occupied and retain many military structures, both from this period and from the time of the Napoleonic Wars.
They count their independence of any ties to France from the year 1204.
Today, the Islands Head of State is Her Majesty the Queen of England who is represented in the Islands by her Lieutenant-Governors. Her role derives from Her status as the successor to the now-defunct Dukedom of Normandy (the Islanders' version of the Loyal Toast, is "The Queen, our Duke". The Islands laws are a mixture of local legislation, customary law (heavily influenced by the English Common Law), Acts of the UK Parliament which have been extended to the Islands and (some) European Union Law in respect of (e.g.) the free movement of people and of goods. The Islands have their own tax systems, currencies (at par with the GBP), banknotes, and individual Parliaments. The relationship with the EU is complex and little understood (they are in the European Community Customs Area, but outside the ambit of fiscal and social legislation for example).
English is spoken throughout the islands but there remain remnants of the old norman patois.
Like the UK, the Channel Islands are outside the Schengen Agreement but form a Common Travel Area with the UK, Republic of Ireland and Isle of Man.