Timeline
Where the game sits on the timeline
The dates that touch this plot
Wikipedia and Konami place Belmont's Curse in 1499. Castlevania III: Dracula's Curse is 1476. Curse of Darkness is 1479. The gaps are 23 years and 20 years. A search snippet that calls the setting the 18th century is wrong for this game. Paris in 1499 is the 15th century.
The classic line around those dates, as the research notes record it, runs Lament of Innocence in 1094, Legends in 1450, Dracula's Curse in 1476, Curse of Darkness in 1479, this game in 1499, The Adventure in 1576, Belmont's Revenge in 1591, and the first Castlevania in 1691. Lords of Shadow is a different continuity and is not mixed into this list.
What to play before, if you want the parents
Trevor and Sypha's fight with Dracula is Dracula's Curse. The 1479 return is Curse of Darkness. You do not need either cartridge to follow Rose's arm. They are the two dates the character page assumes. This game is also described as the 26th mainline entry and a 40th-anniversary release. Those are series-count claims from Wikipedia, not a play order.
What I ran into
I checked the century with a calendar because an 18th-century blurb was everywhere. 1499 is not the 1700s. The correction is the first fact under the dates, not a footnote.
Questions
Is the game set in the 18th century?
No. It is set in 1499.
How long after Dracula's Curse is this?
23 years after 1476, and 20 years after the 1479 events of Curse of Darkness.