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 Prince William, Duke of Cambridge, Catherine, Duchess of Cambridge, Kate Middleton

Dan Kitwood/Getty Images

Kate Middleton is standing by her man—literally and figuratively.

Though a source told E! News Thursday that the Duchess of Cambridge is "disappointed" in Prince William's behavior during his recent boys-only ski trip in Verbier, the royal couple made a public appearance in London Friday to honor soldiers from the Irish Guards on St. Patrick's Day. Middleton, dressed in emerald green, was handed a shamrock, Ireland's national emblem.

Kate was dressed in a custom double-breasted Catherine Walker coat, which featured a black velvet trim on the collar, cuffs and pocket flaps. She accessorized her look with a shamrock pin.

William, meanwhile, wore an Irish Guards frock coat to mark his rank as colonel.

After a parade of the Irish Guards, the royal couple knocked back pints of Guinness to celebrate the holiday. They later met soldiers and their families for lunch in the welfare center of the barracks, where the longest-serving Guardsman in the battalion proposed a toast. Lt. Col. Alex Turner thanked Kate for her support and praised William, saying, "He is our first royal colonel, and so he brought a youthful vitality to the role, which in the past has been a bit more stately."

Later in the afternoon, William, 34, and Kate, 35, will travel to Paris for an official two-day visit. Their Royal Highnesses' visit comes at the request of the Foreign and Commonwealth Office.

 Prince William, Duke of Cambridge, Catherine, Duchess of Cambridge, Kate Middleton

Dan Kitwood/Getty Images

 Prince William, Duke of Cambridge, Catherine, Duchess of Cambridge, Kate Middleton

David Sims/WENN.com

The Duke and Duchess will attend a reception to mark the launch of Les Voisins, hosted by Her Majesty's Ambassador at the British Embassy Paris. The couple will meet young French leaders from the arts, business, fashion, sport and voluntary sectors, as well as military award winners. The royals will attend a black tie dinner, also hosted by Her Majesty's Ambassador, Friday night.

During their visit, the royal couple will also meet outgoing President François Hollande, as well as soccer player Robert Pires and actors Jean Reno, Kristin Scott-Thomas, and Audrey Tautou.

Prince William, Kate Middleton, Guinness

Richard Pohle/The Times/PA Wire

This will mark the first time William has officially visited the French capital, and it comes months before the 20th anniversary of his mother Princess Diana's death. He has traveled privately to Paris in the past, including with his brother Prince Harry, but there are no official plans for him to visit the Pont de l'Alma tunnel or the Flame of Freedom memorial near where his mom died.

The royal couple's visit to Paris has been overshadowed by William's recent ski trip, however. He visited a nightclub in Switzerland with Guy Pelly, James Meade and Tom van Straubenzee, and he was noticeably absent from Monday's Commonwealth Day service at Westminster Abbey, Britain's largest interfaith gathering attended by nearly all members of the royal family.

While Kate is "disappointed" (as is Guy's wife), it should blow over soon. "This will not tear Will and Kate apart by any means," a source tells E! News exclusively, "but William will probably be in the dog house for a bit until this all fizzles out." In the end, the source adds, "They will be fine."

When asked about the Verbier trip, a spokesman for Kensington Palace instead relayed William's feelings about his visit to Paris, saying, "He's very much looking forward to this visit."