Although the movie clearly has rewritten history to make a romance, in reality Jane and Guilford never lived in their own home, nor did they ever live as man and wife in the short time they were together; within a month of the marriage Jane was crowned Queen (and refused to crown Guilford King), and 9 days later they were both in prison, lodged in separate towers, and never had contact again.
Although Jane Grey was offered the chance to spend her final night before her execution with her husband, she refused to have him anywhere near her.
Though Wyatt's Rebellion was a real plot, its purpose was not to put Jane back on the throne, its purpose was to put her cousin, Elizabeth, on the throne.
Jane and Guildford actually hated each other. Their marriage was never actually consummated because Jane was too repelled by him - she was an intelligent young scholar and he was a childish, unpleasant dolt.
Although the film is correct to portray Jane as a precocious and talented scholar, it contains a number of historical inaccuracies. Jane was not a social reformer during her reign as in the film. That type of social reform was not part of political thinking during the Tudor era.