Final answer:
The term for a love affair associated with the 'eternal city' is romantic, which implies an idealized and adventurous form of love derived from the city of Rome.
Step-by-step explanation:
The term for a love affair that comes from the name of the "eternal city" is romantic, which means related to, characterized by, or suggestive of an idealized view of reality. While the word romantic can be broadly associated with love and affection, it specifically refers to a sense of adventure, excitement, and love that often seems too ideal to be true.
The word is derived from the city of Rome, which is often referred to as the "eternal city" and has historically been associated with grandeur, classical beauty, and enduring love.