I can't speak for Robin Hood, but the King Arthur story has historically been extremely popular outside England. In fact a lot of the earliest Arthurian writing comes from French, not English authors. It was Jean Bodel, a French poet from Arras, who first wrote about The Matter of Britain, stating that the story of King Arthur was 'necessary' for educated European rulers to know, along with the stories of Charlemagne and ancient Rome.

Chrétien de Troyes, another French poet, was extremely important to later Arthurian writers. Chrétien is responsible for a lot of the modern conception of Arthur, as he was the first author we know of to talk about Lancelot, Perceval and the Grail Quest - he may have invented them all by himself, or he may have simply been quantifying Celtic myths, but he did an enormous amount to popularise King Arthur - at the time he was probably the world's leading Arthurian writer.

Much later, King Arthur was considered an important enough figure that he was included in the catalogue of the mythical ancestors of the Habsburg dynasty alongside Charlemagne and Barbaraossa.

So, yes, King Arthur was a very important figure whose stories were well known outside the British Isles.

Sources: Andrew Wheatcroft, 'The Habsburgs: Embodying Empire, K. Sarah-Jane Murray, 'A Preface to Chretien de Troyes'.