The city of Geneva is surrounded on all sides by France. The people here speak French, and seem to have much more in common with the French Alpine cultures than with the Swiss Germans. This could be a massive misunderstanding on my part, but as an outside observer I see very little cultural difference between places like, for example, Evian-les-Bains (France), Mont Blanc (France), Lausanne (CH), and Geneva (CH), while this region in general feels very different from Zurich or Bern.
I understand some of the history with the formation of the Swiss Confederation 500 years ago, but it seems strange to me that Geneva was never just swallowed up into France at some point in the last half-millennium. Was that ever an option? Would the Genevois have favored it at any point in their history?
The majority of the citizens of Geneva tended to be at odds with France and its attempts to influence the city most of the time.
Since Switzerland swore eternal neutrality (and renounced their claim to Milan) after their disastrous defeat at the hands of the French and Venetians at Marignano in 1515, France wouldn't attempt to seize the city by force.
France actually did annex Geneva 1798, during the French revolutionary wars. After Napoleon's defeat in 1814, Geneva was readmitted to the restored Swiss Confederation.