Riothamus is so obscure that there is no agreement if this 'Briton' was from the island of Britain (where he is not mentioned in any source or linked to any pre-Anglo Saxon British tribal/ city kingdom) or if he was an emigrant Briton who had settled in the ex-Roman region of Armorica which became known in the C5th and C6th as 'Brittany' (or 'Little Britain', an ironic name considering the modern UK TV comedy sketch series of that name) due to its British settlers. The latter seem to have been moving in in groups from around the 380s AD, and have been linked in legend (how historically is unclear) to the British soldiers in the army of Magnus Maximus, a Roman commander in Britain who usurped the Western Empire's throne in 383 and took an army off to the Continent . Nor is it clear how much of the British emigration to Armorica was a reaction to 'Anglo-Saxon' or 'Jutish' invasions or settlement in Britain, and indeed how large or disruptive the latter phenomenon was in reality - a lot of modern historians now downplay it due to the lack of archaeological evidence of disruption or chaos in post-410 Britain and the amount of 'Romano-Briton' or indeed Neolithic blood in modern British DNA.
All we can say is that if the (few) sources to mention Riothamus, who was operating on the Loire against Germanic (Saxon not Frankish) incomers in the 460s as an ally of the final Western Roman Emperors, were correct that he had about '12,000 ' men this was a large army for the era - and the notion of a British/ Breton warlord with a large army fighting in 'France' in the 460s linked up to Roman Empire politics may have fed into the medieval legends of 'King Arthur' doing this. (The legendary Arthur was however attacking the Roman govt not helping it.) The field of action of the 'Riothamus war' was the Loire valley so quite close to Brittany and also reachable by sea from Cornwall and Devon, whose locals were settling in W Brittany by 500 - hence the new Breton kingdoms of 'Dumnonee' (from the Romano-British Devon tribal kingdom of Dumnonia) and 'Cornouaille'. But as of the 460s there were no Franks, the ancestors of the French, this far SW - the Merovingian dynasty, the later rulers of the first kingdom of France from the time of Clovis (r 481 to 511), only ruled the far NE of France at this point, centred on Tournai in Belgium (whose name comes from the Roman province of 'Belgica', originally part of the lands of the pre-Roman Gallic tribe of 'Belgae'. The rest of the Belgae lived in Hampshire in the UK). The Franks under Clovis only arrived in central France in 486, by destroying the local ex-Roman state , the 'Kingdom of Soissons', ruled by a former Roman general called Syagrius who had succeeded his general father Aegidius - who had taken over the Paris/ Soissons/ Loire / Champagne region when Roman authority collapsed soon after 455. As of this point , SW France was not French either - it was occupied by the wandering tribe of the Visigoths (the ones who sacked Rome in 410) as reluctant Roman allies in 418, and Clovis smashed their army and took it over in 507 at the battle of Vouille. So the 'French' kingdom did not reach the Loire to 486 and did not include SW France as far as the Pyrenees until 507 (or include Provence until much later as the Visigoths in Spain kept it).
Any British (in the sense of non-Germanic , post-Roman) or Anglo-Saxon kingdom would have needed a stable rule over most of the South of the island plus a fleet and a ruler of great ambition and ability plus logistics to have seriously risked intervening in France pre-1066, and the situation in Britain was usually too unstable. The Frankish state, both Merovingian to 751 and Carolingian to 987, was usually too large and well-resourced to make it a viable and worthwhile target, even when the state was divided among feuding royal rivals, and in the C9th and C10th any naval 'control' of the Channel was absent and 'de facto' rested with ephemeral Viking expeditions not with any one kingdom, even a united England which was set up by Alfred's family around 918. (The English kingdom under King Edgar in 959-75 had a large fleet but he only used it in the Irish Sea.) Once the unity of the Frankish kingdom/ 'empire' of Charlemagne split up in 843 the power of a centralised French state rapidly dwindled to the king being 'first among equals' and nominal superior of a multitude of powerful local Counts and Dukes, including from 911 the (Viking origin) Dukes of Normandy - there was no 'centralised French state' to be targeted and conquered and the French kings only really controlled the Paris and upper Seine/ Marne regions plus bits of Picardy and the upper Loire. But a naval expedition by the English state under a capable leader with a strong navy to punish the Normans for harbouring Viking raiders in Norman ports , had the navy set up/ increased by Edgar continued , was possible for a stronger later C10th or early C11th Anglo-Saxon state. In this case, it would have involved Edgar (b c. 943) not dying young in 975 and living to his 50s or 60s or being succeeded by a long-lasting and capable son, not by Aethelred 'Unraed' ('Ill-Counselled' ie 'The Badly-Advised', which became 'The Unready' in later nicknaming).
A strong English state aiding or prompting local French lords into accepting an English-sponsored candidate for power as an aid to local stability plus an English alliance did occur in reality, but only with a dynastically legit candidate who had fled into exile in England earlier and had strong local Fr support - English king Athelstan (r 924/5 to 939) assisted or prompted the return to power of Duke Alan of Brittany in the 930s and King Louis IV 'D'Outremer' ('From Overseas', ie England) in 936. In both cases, the state in question was either leaderless in a civil war or with no clear leader available at the time.
