You can take a totally legitimate research trip. For me, thorough research is an essential part of the writing process. I visited Paris on my own for a research trip a few years ago. Snow covered the city; it was beautiful, lonely and magical and directly influenced a section of the book.
Researching allows you see a city in a new light. Chances are your investigations will take you to parts of Paris you would never have visited otherwise. The everyday streets and off-the-beaten track districts always turn out to be far more interesting than tourist sites.
The food. Need I say more? Paris takes its food very seriously. Centuries-old techniques and practices sit alongside the cutting edge. You can wander into Pierre Hermé for patisserie that is too beautiful to eat, or seek out the best baguette in Paris at Coquelicot. Either way, it's a profound experience.
The history. Paris is teeming with stories. The rise and fall of the aristocracy, revolutions, affairs of the heart… every area of the city is crammed with tales. Which brings me on to:
The inspiration. Simone de Beauvoir. Henri Matisse. Gertrude Stein. Hemingway. Picasso. It's hard not to be inspired when you can walk the same streets and drink in the same cafés and bars as some of the greatest artists and thinkers of the twentieth century.
The markets. For nearly eight hundred years the food market at Les Halles - known as the "belly of the city" fed the whole of Paris. It may be gone now, but other Parisian markets are a treasure trove of sights, smells, tastes and characters. For food, try St Germain, or for endless flea market bargains, you'll want the sprawling "Les Puces" at Porte de Clignancourt.
The thinking time. Arguably, the best way to see Paris is on foot. Far from being a down side, time spent ambling from A to B along boulevards and canals will not only give you a better idea of the city, but some thinking space to reflect on the stories you might set there.
The fluidity. Paris is a restless city. Parisians have been shaping the capital to their will for hundreds of years. From the heyday and decline of districts like La Rive Gauche, to Haussmann's boulevards, to the poverty, anger and social inequality of the banlieues, Paris's identity is at once ingrained and ever-shifting.
The macabre. From the vast Père Lachaise Cemetery to the catacombs at the former Barrière d'Enfer, Paris can be wonderfully ghoulish, which, I'm afraid to say, makes it enticing for a lot of writers. Want proof? Andrew Miller's Pure is a somewhat grisly historical novel about the removal of graves from the cemetery of Les Innocents.
The romance. Part of the joy of setting a book in Paris was to recapture a fragment of a city now lost to time. In fiction at least, we can visit Pigalle, Montmartre and Left Bank as they might have been during the decadent, intoxicating years of the Belle Époque. Yes, Paris has its tourist traps and dark sides, its bygone golden eras and vanished wonders, but somehow, its romance endures.