No, it would not be correct to say that Jude the Obscure by Thomas Hardy "is the last of the Victorian novels and the first of the modern ones." First, this assumes that there is a clear demarcation between Victorian and Modernist fiction and that they can be distinguished as easily as one might distinguish dogs from parrots. That is simply not the case; as Wayne Booth points out, many of the features that some claim to be distinctively modern, such as intrusive narrators, actually are present throughout the entire history of the novel.
Jude the Obscure was serialized beginning in 1894 and first appeared in book form in 1895. As Queen Victoria reigned from 1876 through 1901, this publication date is toward the end of her reign, but it is far from the last novel published in the Victorian era.
In terms of theme, Jude the Obscure addresses the problem of a sensitive young man who is intelligent and self-educated but born into poverty, who fits neither in the class of his origin nor in the educated upper classes. This is a theme one finds in many late Victorian novels, and it addresses the issue of how increasing social mobility ran up against the glass ceiling of entrenched class structures. The treatment of women in this novel is also fairly typical of how late Victorian literature engaged issues of the "new woman" and changing gender roles and expectations. The unrelenting despair and sense of the ultimate fruitlessness of Jude's struggles is something found in other Victorian novels, such as Gissing's New Grub Street.
Technically, the novel is quite typically Victorian, as it is designed for serial publication and written in the third person, with the narrator having full access to Jude's thoughts and some of the thoughts of other characters. The narrator is reliable, time is handled sequentially, and events described realistically.