For your boys names, I don't see any problems with how Joseph, Remy or Edgar would go down, at least looking at what names are popular where I am in London. Remy is particularly nice, Joseph is in common use and Edgar is a little old fashioned but it fits well with similar names that have had a revival. I know boys with all these names.
Pierre and Armand sound more traditionally French and I wouldn't expect them be used by families without a Francophone connection, but anyone would understand them. Auguste is similar I think.
Emil without an -e is easier to use, as with the -e it's easy to mistake for Emilie. But the name itself has a lovely sound.
I don't think that Mayeul is known in the UK.
With your girls names, Iris is very popular in my area but that might be a fluke. Leonie and Beatrice are used but are not overly common and are both lovely.
I like Octavia and people will be familiar with it, but it's unusual. Octavie is pretty but I imagine people might slip into saying Octavia by mistake.
Blanche in an anglophone context sounds like an old-fashioned name from the American South to me and would be surprised to meet a child called that. I know a little Garance in France but I've never heard it in the UK and I think it would be mangled.
In my experience people get used to all kinds of names though, so even those that seem more difficult to use here wouldn't be impossible. I also wouldn't worry about avoiding names that have accents in French and don't in English. Mine does that and it's not ever caused a problem.