Use of with

Literal translations can sound odd - 'one should not speak mouth full' sounds unusual in English. As Jim notes, the translation is how the expression is used in English - it is a 'free' translation, although in this case very close to a literal one also.

Similarly with "on ne doit pas manger la bouche ouverte". 

Hi Joseph,

The verb parler can be used intransitively (without an object) so there is no direct word for word translation in the structure that you have given.

"On ne doit pas parler la bouche pleine" -->  "One should not speak with one's mouth full" is the English "understood" translation.

Hope this helps.

Jim