We just don't know, there's no historical evidence of its origin.

The battle of Agincourt (1412 - origin of archers story) story only arose in the 19th century, or rather we don't have any recorded instances of the story pre 19th century.

In the novel, 'the white company' (1891), by Sir Arthur Conan Doyle, he mentions the English archer V sign, stemming from battles with the French. Which whilst we can’t 100% prove to be the insult v sign, it would be a safe bet to say that it is. So, we can at least place the Agincourt myth to have at least originated around then.

That aside, the Agincourt story it is said to be incorrect because it was customary to just execute prisoners immediately, as they held no worth, so the two fingers cutting would have been incredibly unlikely, especially on mass, not to mention you need three fingers to use a longbow so if they did cut off fingers, the English would have cut three, not two.

The first recorded, 100% correct, use of it is only in 1901, when an ironworks labourer in Rotherham (England) is seen using the sign, on film, to show that he didn't want to be filmed: second from right.

Before this we don't have any concrete recorded evidence (pictures, drawings, detailed descriptions etc) of it.

Though since the sign in the film was well understood, it's safe to say that the sign at least goes back to the Victorian period.