ORIGIN Old French & mod. French from Latin Saxon(n-), pl. Saxones = Greek Saxones from West Germanic (whence Old English pl. Seaxan, Seaxe, Old Saxon, Old High German Sahso, German Sachse), perh. From base of SAX noun.

Saxon seems to have originally referred to a member of a Germanic people living in northern Germany in the early CE period.

Part of these people occupied some of southern Britain in the 5th and 6th Centuries and where also called Saxons. Loosely, it referred to any of the Germanic people who settled in Britain or an Anglo-Saxon. This is how it was used in Middle English.

By Late Middle English the term also became an adjective and referred to the Saxon language.

In the Mid 17th Century it began to be used to describe the people of Saxony in Germany.

In the early 1800s it was used to refer to an English person who was presumed to be of Saxon descent. This was especially used among Celtic speakers to refer to an English person as distinct from a Welsh or Irish person.

At the same time it also began to be used to describe a Lowland Scot as distinct from a Highlander (Sassenach), as well as any person of English or British descent as opposed to one of Latin descent.

The source for all this is the Oxford English Dictionary.