Origins
Romance began as a language label, not a feeling. The word comes from Vulgar Latin *rōmānicē, meaning 'in the Roman tongue' — the everyday speech of the former Roman Empire, as opposed to formal Latin. A romance was a text written in the vernacular: in French, for a French audience.
These vernacular narratives were not legal documents or theological treatises. They were adventure stories — tales of knights on quests, damsels in towers, enchanted swords, and forbidden love. The Arthurian legends, the Chanson de Roland, the stories of Lancelot and Guinevere were all romances: narratives in French.
The word absorbed the character of the stories it described. By the 14th century, romance meant not just 'a text in French' but 'a tale of adventure and wonder'. By the 17th century, the love element had overtaken everything else. A romance was a love story, and romantic meant 'inclined to love and idealism'.
Latin Roots
French preserves the older meaning more clearly. Un roman is simply 'a novel' — any novel, not necessarily a love story. Spanish romance means 'a ballad'. The literary sense endures in 'the Romance languages' — French, Spanish, Italian, Portuguese, Romanian — languages that descended from Roman speech.
The chain from 'Roman' to 'love story' is a parable of how language shifts. Rome became a language. The language became a genre. The genre became an emotion.