Prince William managed to crack a smile upon arriving in Paris this afternoon (17 March) for a fleeting 24-hour visit, meeting with French President Francois Hollande at the Elysee Palace just moments after stepping off a private jet.

The Duke of Cambridge, 34, may have been told to put on a happier front following his disgruntled appearance at a St Patrick's Day parade in Hounslow, West London, earlier in the day.

It marks the first engagement since his highly reported on 'lads only' ski trip to Verbier in the Swiss Alps where he was videoed 'dad dancing'.

Demonstrating that all is well between him and wife Kate Middleton, William showed some teeth and stood alongside her as they chatted to President Hollande, appearing fully recovered from the Swiss trip.

The couple's body language was rather rigid throughout the appearance as they stood side by side in a poised position, with the duchess widely smiling from ear-to-ear while their pictures were being taken.

Middleton, 35, had no time to change outfits in between the Irish Guards event this morning and her arrival in Paris, looking effortlessly chic in the black-trimmed forest green coat dress by the late Princess Diana's favourite designer, Catherine Walker.

There was a subtle difference in her outfit, however, as she let her hair down and removed the matching green hat from the morning engagement, instead showcasing her trademark blow-dried loose hairstyle.

Duke and Duchess of Cambridge
Duke and Duchess of Cambridge

The Duke and Duchess of Cambridge's trip to Paris has a substantial political significance as the royals serve as goodwill ambassadors for Britain at the request of the Foreign Office following the Brexit vote. The aim is to strengthen Anglo-French relations ahead of the triggering of Article 50.

An FCO source claims: "The British Royal Family are some of the most important diplomats we have," and that they will play a major part in our "soft diplomacy efforts."

The duke and duchess' first engagement was with President Hollande at The Elysee Palace after they jetted into the French capital on a private plane, and the lavish building is where William and the president will hold talks.

Duke and Duchess of Cambridge
Prince William, prior a meeting with French President Francois Hollande at the Elysee Palace Pascal Le Segretain/Getty Images

William has travelled privately to the French capital in the past – including with his brother Prince Harry – but there are no plans for him and the duchess to visit the Pont de l'Alma tunnel or the Flame of Freedom memorial close to where his mother died.

William and Kate will also be guests of honour at a British embassy reception called "Les Voisins" ("neighbours") to celebrate cultural ties between the UK and France. They will meet young French leaders at the glamorous affair from the worlds of arts, sport, fashion and business, as well as young military award winners.

kate middleton
France's President Francois Hollande (R) with Prince William and his wife Kate, the Duchess of Cambridge at the Elysee Palace THIBAULT CAMUS/AFP/Getty Images

The royals will later meet first responders at the scene of the 2015 terrorist attacks at the Bataclan theatre in Paris which left 130 people dead, and the lorry attack in Nice on Bastille Day last year.

The trip includes tickets to the Six Nations rugby match between France and Wales on Saturday (18 March) along with a meeting with Bataclan massacre survivors.

Following the Paris tour, the couple will visit Germany and Poland in July in a similar bid to bolster relations with EU nations in post-Brexit Britain, reports The Guardian.

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France's President Francois Hollande (R) poses with Britain's Prince William and his wife Kate, the Duchess of Cambridge, in the gardens of the Elysee Palace THIBAULT CAMUS/AFP/Getty Images

Of the Paris visit, royal expert Richard Fitzwilliams is keen to know what gifts will be exchanged between President Hollande and the royals.

He told IBTimes UK: "It will be interesting to see what gifts are exchanged. In 1972 President Pompidou presented the Queen and Prince Philip with a hideous 6-foot giant wine cooler in the shape of a grasshopper. In 2015 in Germany the Queen was presented with a dreadful painting of her as a girl on a blue horse and which included her father whom she did not recognise, a dreadful choice of gift."

kate middleton
Prince William and Kate Middleton are all smiles in Paris THIBAULT CAMUS/AFP/Getty Images