In the extract I found on Youtube (https://www.youtube.com/watch?v=NOP1YHtXYsk), Pontius Pilate is made to speak French in exactly such a way. /ʀ/ is replaced by /w/, sometimes by English /ɹ/, or by nothing :
- Alors, terroriste hébraïque /alo: tewowistebwaik/
He sounds like a mix between somebody from the French Antilles, a bit like the pirate lookout from Asterix, and an Englishman speaking French.
If you wanted to use something else, you'd have to have him speak with a really thick accent that borders on unintelligibility since sometimes the centurion doesn't get what he's saying. The problem is that he's supposed to have a speech impediment, or is he really? According to Gimson and Cruttenden :
some speakers labialize /r/ whatever the following vowel. In extreme cases, lip-rounding is accompanied by no articulation of the forward part of the tongue, so that /r/ is replaced by /w/ and homophones of the type wed, red are produced. Alternatively a labiodental approximant [ʋ] may be heard as a realization of /r/ or even for both /r/ and /w/. Pronunciations of this sort were a fashionable affectation in the nineteenth and early twentieth century; and can still be heard as such from some elderly people educated at major public schools.
Cleese and Idle were educated at Oxford, Jones and Palin at Cambridge, they might have had dealings in the 60s with older dons that spoke in such an affected way.
In any event, the solution they chose for the dubbing I find is quite funny.