Jennifer Lopez and Ben Affleck Jet Off to Paris After Tying the Knot at Las Vegas Chapel

Laurent Salmon/KCS PRESSE/MEGA Jennifer Lopez and Ben Affleck

Jennifer Lopez and Ben Affleck are celebrating being officially husband and wife in the city of love –– Paris, France!

Dinner guests at Le Matignon Restaurant were surprised to discover the newlyweds arriving for dinner on Thursday night.

The couple arrived at Le Bourget airport by private plane just hours earlier, a source tells PEOPLE. The "Love Don't Cost a Thing" singer and Argo director wasted no time stepping out to kick off their post-nuptial celebration.

Hitting the restaurant near the Champs-Élysées, the world's most celebrated newlyweds held hands while asking for a table on the outside terrace. "They just showed up," one surprised eyewitness tells PEOPLE. "He looked like a typical American except he had on a jacket and tie in this heat."

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Lopez, 52, looked radiant in a gorgeous red dress, wearing her hair in a loose updo with face-framing layers while keeping her glam fresh and natural.

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The couple stayed approximately two hours at the upscale restaurant and dance club before heading back to their hotel on a romantic nighttime drive.

On The JLO Ben Affleck and Jennifer Lopez

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Months after revealing their engagement in April, the couple obtained a marriage license in Clark County, Nevada, over the weekend, according to court records obtained by PEOPLE.

The duo then wed in a "super, super small" ceremony, a source told PEOPLE. "They just wanted to be married so they got married."

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In a conversation with PEOPLE earlier this week, Ryan Wolfe, the lead pastor at Grace Christian Center of Las Vegas, said the couple had "their own vows that they wanted to share with one another" during the surprise ceremony held at A Little White Wedding Chapel on Saturday night.

RELATED VIDEO: Jennifer Lopez and Ben Affleck Jet Off to Paris After Tying the Knot at Las Vegas Chapel

While Wolfe kept the actual vows private, he said "they had their own words and they were beautiful words to each other."

"It was an emotional moment they shared with one another," Wolfe added. "You can definitely see the love that they have for each other."