The parentheses are part of the speech; if there could be any doubt, the context makes it unquestionable:
—Еh bien, mon prince. Genes et Lucques ne sont plus que des apanages, des поместья, de la famille Buonaparte. Non, je vous previens, que si vous ne me dites pas, que nous avons la guerre, si vous vous permettez encore de pallier toutes les infamies, toutes les atrocites de cet Antichrist (ma parole, j'y crois) —je ne vous connais plus, vous n'etes plus mon ami, vous n'etes plus мой верный раб, comme vous dites. Ну, здравствуйте, здравствуйте. Je vois que je vous fais peur, садитесь и рассказывайте.
Так говорила в июле 1805 года известная Анна Павловна Шерер...
Anna Pavlovna speaks mixed French and Russian, but when Count Tolstoy lifts his voice he writes in Russian only.
What are the parentheses there for? —Representing dialogue plausibly is a constant difficulty for writers of fiction and drama, because the speech even of highly educated people appears almost incoherent when it is reduced to writing, deprived of its non-verbal cues, and divorced from the context which the speakers share.
Writers with “good ears” strive to reproduce the rambling, disjunct, paratactic quality of real speech; but if they reproduce it too accurately, too literally, it may be unintelligible to readers, or give a false sense of characters’ linguistic incompetence. This is particularly true in fiction, where the reader must work his own way through the dialogue, without the benefit of well-rehearsed real-time interpreters.
One very potent instrument for bringing clarity to dialogue is a liberal use of punctuation. Not only quotation marks, but asterisks, dashes, ellipsis points† and parentheses serve several purposes which are not pursued in ordinary discursive prose. Their profusion provides a strong visual cue that the passages where they are used occupy a different register. They are powerfully disjunctive, emphasizing the fragmentation of speech flow into isolated phrases and signalling abrupt changes of tone and rhetorical direction. At the same time, however, they are helpfully conjunctive: for they also bracket passages, marking off sections of the flow as at least internally coherent and meaningful.
So, no, you probably don’t want to substitute commas for this pair of parentheses—that would reduce this disjunction to the same level as that which marks other comma-bracketed phrases, and lose the distinction Count Tolstoy wants to mark here. But you might prefer to employ dashes, as in Nathan Haskell Dole's translation:
“Well, prince, Genoa and Lucca are now nothing more than the apanages, than the private property of the Bonaparte family. I warn you that if you do not tell we are going to have war, if you still allow yourself to condone all the atrocities of this Antichrist—on my word I believe he is Antichrist—that is the end of our acquaintance; you are no longer my friend, you are no longer my faithful slave, as you call yourself.
† This essay offers a fascinating account of the history of the use of various marks of ellipsis.