Gareth Rees's answer is correct (he just beat me to it
:-)), showing how Mr Rochester's story indicates his lover's infidelity as clearly as it could be without him actually finding them in flagrante delicto. However, since your question seems to be casting doubt on Mr Rochester's status as a reliable narrator, I thought it would be interesting to examine the issue of whether or not, or to what extent, we can take his story at face value.
Within the frame of the narrative, Mr Rochester is a reliable narrator. Although Jane doubts and mistrusts him in various ways throughout the story, it never occurs to her to believe he has fabricated or misrepresented his own past. Indeed, soon after the conversation in which he tells her of Celine Varens, her thoughts show that she disapproves of some of his past actions but doesn't think to disbelieve his story:
And was Mr. Rochester now ugly in my eyes? No, reader: gratitude, and many associations, all pleasurable and genial, made his face the object I best liked to see; his presence in a room was more cheering than the brightest fire. Yet I had not forgotten his faults; indeed, I could not, for he brought them frequently before me. He was proud, sardonic, harsh to inferiority of every description: in my secret soul I knew that his great kindness to me was balanced by unjust severity to many others. He was moody, too; unaccountably so; I more than once, when sent for to read to him, found him sitting in his library alone, with his head bent on his folded arms; and, when he looked up, a morose, almost a malignant, scowl blackened his features. But I believed that his moodiness, his harshness, and his former faults of morality (I say former, for now he seemed corrected of them) had their source in some cruel cross of fate. I believed he was naturally a man of better tendencies, higher principles, and purer tastes than such as circumstances had developed, education instilled, or destiny encouraged. I thought there were excellent materials in him; though for the present they hung together somewhat spoiled and tangled. I cannot deny that I grieved for his grief, whatever that was, and would have given much to assuage it.
We are clearly intended, like Jane, to take his story at face value.
Even after she discovers that he has lied to her about being a bachelor, she is quick to forgive him in her heart, and doesn't think to doubt the rest of his life story.
Oh, never more could it turn to him; for faith was blighted—confidence destroyed! Mr. Rochester was not to me what he had been; for he was not what I had thought him. I would not ascribe vice to him; I would not say he had betrayed me; but the attribute of stainless truth was gone from his idea, and from his presence I must go: that I perceived well.
Reader, I forgave him at the moment and on the spot. There was such deep remorse in his eye, such true pity in his tone, such manly energy in his manner; and besides, there was such unchanged love in his whole look and mien—I forgave him all: yet not in words, not outwardly; only at my heart’s core.
The intent of the story is that Mr Rochester is an essentially good man - with plenty of past indiscretions, to be sure, but that he is honest except for the one great secret he kept hidden - from everyone, not just his new intended bride - for so many years.
However, there are alternative readings of the story. It is possible to construe Mr Rochester in an entirely different manner: to argue that Jane's belief in him was due more to her infatuation than his essential honesty, and to cast a different light upon his life. Even his first wife Bertha, seemingly the villain of the piece, can be viewed sympathetically, her insanity the result of ill-treatment rather than a mental defect. For more on this reading of the novel, I refer you to Wide Sargasso Sea, a retelling from Bertha's point of view. (I haven't read it myself, but it sounds interesting!)
Under this interpretation, it is possible to disbelieve almost anything Mr Rochester says about his past. If his version of Bertha - the insane woman devoid of virtue whom he was tricked into marrying by his family and hers - is a lie, then so also could be his version of Celine Varens. Perhaps she was true and faithful to him, and he merely grew tired of her, moved on to other women, and made up the story about her unfaithfulness to make himself look better. We only have his word for it, and if his word comes into doubt, then so does all of his past life except the parts and details which have been somehow confirmed by other means.