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.

The possible replacement of r’s by no sound at all as would the French « muscadins » do in France’s post revolutionary days (revolution of 1789) would constitute an anachronism and as well would not have been convenient for r beginning words : those would not have been understandable. Their pronunciation was in fact an imitation of the English r which corresponded to the softened r the English have. Also, if the same sound had been used (/w/) many words would have been impossible to make out; that’s probably a reason for giving up on transcribing this feature. Moreover, it is not really far fetched to think that the proximity of that pronunciation with that of r’s by African populations could have been misinterpreted by a great part of the audience (mixture of civilisations); it’s a pronunciation that has enjoyed for a long time in France an unflattering reputation, even if it was not characteristic of any hostility as this ethnic particularity relative to pronunciation served only the purpose of the life and soul of the party and other entertainers in cheering up the insouciant listeners, and that is closely associated with that context. Other than those two options, the little known and impractical muscadin’s quirk of pronunciation and the African particularity of using an allophone of /w/, well known but specific to a given context, there is nothing available; it would have been necessary to resort to invention. The reason for the ambiguity as regards the substitution of /r/ with /w/ lies in the singleness of the language feature : when someone impersonates extravagantly a foreign way of speaking they use a good number of all the features of the language even if they are quite distorted and that helps in identifying ethnicity and also, often no one pays attention to the meaning of the words that amount to no more than gibberish; however unique features as sole modification in a piece of speech are largely lumped into one single allophonic variety in the untrained ear.