It's a little earlier, but as an interesting example, Æthelberht of Kent, the first Anglo-Saxon king in England, was married to Bertha, the daughter of the Merovingian king Charibert. He appears to have resisted her attempts to convert him until the Augustinian mission of 590 and this may have been because converting to a Papal mission would establish an independent church in Kent whilst being converted by Charibert would have made Kent subservient to his rule.

The Anglo-Saxon Chronicle makes no reference to the coronation of Charlemagne in 768 or his taking of Italy in 774 or coronation as Holy Roman Emperor in 800, marking only in 782 that 'In this year the Old Saxons and the Franks fought together' (the Battle of the Suntel Hills and the Massacre at Verden). Charlemagne's death in 814 is mentioned but only in passing. Other events in Europe, such as the Roman mob attacking Pope Leo in 799, are recorded, which suggests that perhaps the rise of the Carolingians wasn't seen as particularly significant given the complex political situation within England at the time.

Alcuin of York's letters show that towards the end of his reign, Offa attempted to foster closer diplomatic ties with the Carolingian and he and Charlemagne exchanged letters. Charlemagne proposed that his son marry one of Offa's daughters, and Offa suggested that in turn his son Ecgfrith marry one of Charlemagne's daughters, which apparently did not go down well and triggered an attempted closure of Frankish ports to English ships. The matter was eventually resolved, and correspondence between the kings discussed matters such as pilgrims' rights and trade between the kingdoms. These survive in English Historical Documents Vol. 1 edited by Dorothy Whitelock. Despite the huge disparity in their political power, Charlemagne refers to Offa as 'brother' suggesting that, diplomatically at least, there was an attempt to foster a relationship as equals. Offa certainly reformed his coinage along Carolingian lines. However, Charlemagne may have sought to underwhelm Offa and place a more compliant king on his throne as he did shelter dissidents against Offa at his court.

In later centuries, the balance of power seems to have changed somewhat. Carolingian coinage was weak, especially compared to the later English penny, and English coinage was standardised at a different silver weight than Carolingian equivalents. Carolingian currency was excluded from England, being collected and reforged if found. In 924, Athelstan married his sister Edith 'to the son of the king of the Old Saxons', the future Otto the Great, suggesting an alliance between two nascent kingdoms, England and Ottonian Germany.

Kirby, D.P., The Earliest English Kings

Whitelock, D. (ed.), The Anglo-Saxon Chronicle

Whitelock, D. (ed.), English Historical Documents Vol. 1

Stenton, F., Anglo-Saxon England