It's never definitively said whether or not Mr. Rochester is Adèle's father. He acknowledges that it's technically possible, but he very much doubts it. He does not recognize her as his daughter, but has taken responsibility for her as his ward.
The first time that the reader learns about Adèle Varens in Charlotte Brontë's Jane Eyre is in Chapter 11, shortly after Jane's arrival at Thornfield Hall. Jane mistakenly believes that she will be tutoring Mrs. Fairfax's daughter, but Mrs. Fairfax corrects her.
“Miss Fairfax? Oh, you mean Miss Varens! Varens is the name of your future pupil.”
Mrs. Fairfax converses amiably with Jane about Thornfield and its residents, and she mentions that "just at the commencement of this autumn, little Adela Varens came and her nurse." Mrs. Fairfax is the only person in the Thornfield household, of which she is the housekeeper, who refers to Miss Varens as "Adela." In her conversation with Adèle that morning, Jane learns that Adèle's mother "is gone to the Holy Virgin."
Adèle makes no mention of her father. She does, however, mention "Mr. Rochester," the owner of Thornfield Hall, who she knew when her mother was alive and who was always very kind to her "and gave me pretty dresses and toys." Adèle says that when her "mama" died, Mr. Rochester "asked me if I would like to go and live with him in England." She agreed, but she regrets that she never sees him.
It's not until Chapter 15 that Jane learns more about Adèle from Mr. Rochester. He says that Adèle is the daughter of a French opera-dancer, Céline Varens, with whom he had once enjoyed what he calls a "grande passion." Mr. Rochester set up Céline Varens as his mistress but later discovered that he wasn't her only paramour. Mr. Rochester turned her out, but not before "the Varens," as he sometimes called Céline, produced Adèle, who, she claimed, was his daughter.
Mr. Rochester concedes there is a possibility that Adèle might be his daughter, though he claims to see no resemblance between them: "I see no proofs of such grim paternity written in her countenance." Mr. Rochester remarks that his dog, Pilot, looks more like him than Adèle does.
Mr. Rochester explains that some years later, Céline Varens abandoned Adèle and ran away to Italy "with a musician or singer." Mr. Rochester reiterates that there is "no natural claim on Adèle’s part to be supported by me," and he asserts "I am not her father." Hearing that Adèle was left destitute, however, Mr. Rochester took responsibility for the child, and "took the poor thing out of the slime and mud of Paris, and transplanted it here, to grow up clean in the wholesome soil of an English country garden."