What influenced the rise of the novel in the eighteenth century?
First, let's define the novel as an extended narrative in prose. Second, my answer assumes that your question focuses on the rise or development of the novel during the 18thC. in Britain.
If we examine the novels of Samuel Richardson, Daniel Defoe, Henry Fielding, Tobias Smollett, Laurence Sterne, Fanny Burney, and Ann Radcliffe, a common ancestor for many British novels in the 18thC. are two Spanish works--often considered the first of the picaresque novels--Cervantes' Don Quixote (1605) and the anonymous Lazarillo de Tormes (1554), whose heroes go through a series of often comic adventures. A French novel, Gil Blas (1715), by Le Sage, also influenced several British novelists--Fielding, Richardson, Sterne and Smollett (who translated the book in English)--whose picaresque heroes resemble the main characters in earlier Spanish and French works.
Even though the 18thC. British novelists were influenced by these earlier continental works, the highest evolution of the novel form occurs in Britain where the combination of comedy and drama in prose captured the reading public's attention (along with a lot of controversy about the value of the novel as a genre). The wild popularity of the novel in England drove the economics for many talented writers, who could earn a decent living by writing novels, and many female writers became successful novelists during the century.
Perhaps the primary influence for the development of the novel, however, is that the novel form provided a huge canvas for writers to depict increasingly complex human experience in a society that was undergoing radical and faced-paced changes all aspects of life. One could argue that the novel form was perfectly suited for the times in which the form fully evolved.