I was thinking about this thread the other day, with reference to Romani, and I think it's a little bit about expectations rather than mutual comprehensibility as such.
Romani is a European language of Indian origin: there are plenty of Romani words that are still recognizably Indian, but there are also loads that come from Greek, Romanian, and Slavonic languages - even in the Romani that used to be spoken in Wales. So, for example, if you count to ten in Romani to a Hindi speaker, they'll recognize 1-6 and 10, but look really puzzled at 7, 8, and 9, which are Greek. You really can't speak continuous Romani to a speaker of any other Indian language and expect to get particularly far, but there are odd words and short sentences you can pick and choose that are comprehensible from Wales, through Persia and Afghanistan to India.
So there's a book I have about English Romani in the nineteenth century, when it was starting to turn into a mix of Romani and English, like British Romani Gypsies might use today (think Wenglish on steroids). In it, one of their main informants, Sylvester Boswell, is asked about European Romanies, and he basically just goes on about how different they are, including not understanding each other at all. But then, at another point, he tells how he met a Bengali speaker in Britain and they understood each other perfectly! (Which I don't really believe.)
What I think is that if you meet another Romani (Welsh) speaker you expect to be able to understand each other, speaking the same language; and if there are big enough differences of dialect to make it difficult, the main thing you're aware of are the difficulties. But you know that no-one else speaks anything remotely like Romani (Welsh) - all the other languages you come across in your normal life are completely unlike it. And then you come across someone speaking Bengali (Breton), and find that you can sort of muddle through a bit (nose! hair! milk! one, two, three! Wow!) and it's astonishing - we got on like a house on fire!
So I suspect that if your dad spoke Welsh and French and English, and the onion sellers Breton and French and (presumably) some small smattering of English and / or Welsh, they'd have muddled through somehow, quite possibly with a certain amount of Welsh in the mix, and been honestly impressed with how well they communicated.