It is the prince's first official visit to the French capital since his mother Diana died there in a car crash in 1997.
William, who is second-in-line to the throne, and his wife are acting as goodwill ambassadors for Britain just as the country prepares to trigger the formal process of leaving the European Union.
At a reception for young French entrepreneurs to launch a celebration of Franco-British links called "Les Voisins" (Neighbours), the 34-year-old prince said the two countries had much in common.
"This partnership will continue despite Britain's recent decision to leave the European Union," William said.
"The depth and the breadth of our cooperation will not change."
The couple met French President Francois Hollande soon after arriving in the capital and on Saturday they are due to meet victims of the November 2015 terror attack on the Bataclan concert hall in Paris.
The couple will also attend a Six Nations rugby match between France and Wales at the Stade de France on Saturday.
The trip comes as William faces criticism in the British media for missing a Commonwealth celebration to go skiing with friends.
British tabloids have questioned his work ethic after a video emerged of him dancing at a nightclub during the holiday in the exclusive Swiss resort of Verbier.
Maeva Tordo, a French woman who runs a company that encourages the creation of start-ups, had a conversation with the prince punctuated by laughter at a reception at the British embassy.
"He has a good sense of humour. You can feel that he would like to set up a start-up himself. But we didn't ask him about his dancing," she told reporters afterwards.
Kate in McQueen
In the world's fashion capital, Kate wore a sleeveless v-neck black dress by Alexander McQueen before changing into a grey-blue gown by British designer Jenny Packham later in the evening.
At a star-studded black-tie dinner at the ambassador's residence, Kate was seated next to "Godzilla" star Jean Reno, while her husband had French actress Audrey Tautou and Kristin Scott-Thomas, the British actress who lives in Paris, for company.
Newly appointed Givenchy designer Clare Waight Keller and former Arsenal and France footballer Robert Pires were also among the guests.
They were served a starter of langoustine before a main course of roast lamb -- but to the French media's amusement, the traditional British mint sauce for the meat did not feature.
William read a message to the 150 guests from his grandmother Queen Elizabeth II in which she recalled it was nearly 70 years since she had first visited France.
"I retain the fondest of memories of my five state visits over the years, as well as an enduring affection for this beautiful country and its people," she said.
In a possible reference to Brexit, she said "much has changed since my first visit" but concluded that "the ties between our nations have stood the test of time and will, I am sure, continue to prosper."
French magazines have described the royals' trip, organised at the request of the British foreign ministry, as a charm offensive by Britain as it prepares to break away from the EU.
Gala magazine called them "the glamorous card to make you forget Brexit" -- a tactic that will also be tested when they travel to Germany and Poland in July.
Although no official commemoration is planned during the trip, it will be impossible to escape the poignancy of Diana's eldest son visiting the city where she died on August 31, 1997.
William was just 15 and his brother Harry 12 when their mother and her boyfriend Dodi Al-Fayed were killed after their Mercedes crashed in central Paris as it was being pursued by press photographers.
Their French chauffeur Henri Paul, who was over the legal blood alcohol limit, also died.
Officials say there are no plans for the prince to visit the crash site in the Pont de l'Alma tunnel.