Telling someone they are "nice" once meant calling them a fool.
The word starts as Latin nescius, "not knowing," built from ne-, "not," and a form of scire, "to know." The same scire gave English "science." Old French turned it into nice in the 1100s with senses such as careless, clumsy, weak or simple. English borrowed it in the late 1200s, and at first it meant foolish or ignorant. Merriam-Webster adds wanton and dissolute among the early senses.
Then the word began a long, winding drift. Etymonline sketches the path. Timid or faint-hearted is recorded before 1300. By the late 1300s it meant fussy or fastidious, and by about 1400 it could mean dainty or delicate. In the 1500s it meant precise or careful, which survives in "a nice distinction" and "nice measurements."
The pleasant sense is recent. Etymonline dates "agreeable" or "delightful" to 1769 and "kind" or "thoughtful" to 1830. The etymologist Ernest Weekley called the career of the word extraordinary, even for an adjective. Etymonline adds that 1500s and 1600s uses are often ambiguous about which sense was meant.
By the early 1800s the word was already seen as overused. Jane Austen poked fun at it in Northanger Abbey in 1803, and H. W. Fowler complained in 1926 that it had become too great a favorite with the ladies, a vague word of mild agreeableness.
The word has relatives in change. Etymonline groups nice with fond, innocent, lewd, silly and simple as words whose meanings moved a long way from where they began.
One more note: the French city of Nice, on the Mediterranean, has nothing to do with the adjective. Etymonline derives its name from Greek nikaios, "victorious," from nikē, "victory."