Mary-Kate Olsen, 29, and fiance Olivier Sarkozy, 46, hold hands in the Hamptons

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Mary-Kate Olsen and Olivier Sarkozy Step Out For Hamptons Horse Show

Looks like Mary-Kate Olsen and her much older man, French banker Olivier Sarkozy, are still going strong and not shy about showing some PDA.

The couple was snapped at the 2015 Hampton Classic Horse Show in New York on Thursday, holding hands at the posh event. The 29-year-old former Full House actress looked like an equestrian herself in a white polo and khaki pants, while her 46-year-old fiance -- the half-brother of former French president Nicolas Sarkozy -- went casual in jeans and a striped button-down.

WATCH: Mary-Kate and Ashley Olsen Talk 'Full House' Spinoff -- You Got It, Dude!

Mary-Kate and Olivier first stepped out together in 2012, and reportedly got engaged in late February, though the notoriously private Mary-Kate has never confirmed any news about her personal life. Last September, Luckymagazine reported that the two had already tied the knot, citing an "anonymous, well-connected source," after they were spotted wearing matching thin gold wedding rings in the Hamptons.

If true, it would mark Mary-Kate's first marriage and Olivier's second. He was previously married to author Charlotte Bernard, and has two children with his ex-wife -- son Julien, and daughter Margot.

See more of the couple here:

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Mary-Kate Olsen and Olivier Sarkozy
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Mary-Kate Olsen, 29, and fiance Olivier Sarkozy, 46, hold hands in the Hamptons
NEW YORK, NY - NOVEMBER 20: Olivier Sarkozy and Mary-Kate Olsen attend the Indiana Pacers vs New York Knicks game at Madison Square Garden on November 20, 2013 in New York City. (Photo by James Devaney/WireImage)
NEW YORK, NY - NOVEMBER 09: Mary-Kate Olsen and Olivier Sarkozy attend the Dallas Mavericks vs New York Knicks game at Madison Square Garden on November 9, 2012 in New York City. (Photo by James Devaney/WireImage)
NEW YORK, NY - NOVEMBER 20: Olivier Sarkozy and Mary-Kate Olsen attend the Indiana Pacers vs New York Knicks game at Madison Square Garden on November 20, 2013 in New York City. (Photo by James Devaney/FilmMagic)
Mary-Kate Olsen and boyfriend Olivier Sarkozy in the audience at The Cutting Room to see Ronnie Wood of the Rolling Stones perform with guitarist Mick Taylor, drummer Simon Kirke and keyboardist Al Cooper on Thursday, Nov. 7, 2013 in New York. (Photo by Evan Agostini/Invision/AP)
EAST HAMPTON, NY - AUGUST 24: Olivier Sarkozy and Mary Kate Olsen attend 4th Annual Apollo In The Hamptons Benefit on August 24, 2013 in East Hampton, New York. (Photo by Shahar Azran/WireImage)
NEW YORK, NY - NOVEMBER 09: Mary-Kate Olsen and Olivier Sarkozy attend the Dallas Mavericks vs New York Knicks game at Madison Square Garden on November 9, 2012 in New York City. (Photo by James Devaney/WireImage)
NEW YORK, NY - SEPTEMBER 1: Mary-Kate Olsen and her boyfriend Olivier Sarkozy, brother of former French President Nicolas Sarkozy attend Day 8 of the 2014 US Open at USTA Billie Jean King National Tennis Center on September 1, 2014 in the Flushing neighborhood of the Queens borough of New York City. (Photo by Jean Catuffe/GC Images)
NEW YORK, NY - SEPTEMBER 01: Olivier Sarkozy and Mary-Kate Olsen attend day 8 of the 2014 US Open at USTA Billie Jean King National Tennis Center on September 1, 2014 in the Flushing neighborhood of the Queens borough of New York City. (Photo by Uri Schanker/GC Images)
NEW YORK, NY - SEPTEMBER 01: Olivier Sarkozy and Mary Kate Olsen attend day 8 of the 2014 US Open at USTA Billie Jean King National Tennis Center on September 1, 2014 in New York City. (Photo by Uri Schanker/GC Images)
NEW YORK, NY - OCTOBER 08: Mary-Kate Olsen, Olivier Sarkozy and David Kratz attend 2013 'Take Home A Nude' Benefit Art Auction And Party at Sotheby's on October 8, 2013 in New York City. (Photo by Monica Schipper/Getty Images)
NEW YORK, NY - NOVEMBER 09: Mary-Kate Olsen and Olivier Sarkozy attend the Dallas Mavericks vs New York Knicks game at Madison Square Garden on November 9, 2012 in New York City. (Photo by James Devaney/WireImage)
NEW YORK, NY - NOVEMBER 20: Olivier Sarkozy and Mary-Kate Olsen attend the Indiana Pacers vs New York Knicks game at Madison Square Garden on November 20, 2013 in New York City. (Photo by James Devaney/WireImage)
NEW YORK, NY - DECEMBER 14: Olivier Sarkozy and Mary-Kate Olsen attend the Atlanta Hawks vs New York Knicks game at Madison Square Garden on December 14, 2013 in New York City. (Photo by James Devaney/WireImage)
NEW YORK, NY - NOVEMBER 03: Olivier Sarkozy and Mary-Kate Olsen attend the Minnesota Timberwolves vs New York Knicks game at Madison Square Garden on November 3, 2013 in New York City. (Photo by James Devaney/WireImage)
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Mary-Kate actually talked about possibly designing her own wedding dress last May -- but stressed that there was no rush. "I'm, like, not even there yet," she told WWD. "I think it may be a matter of getting five or six or making two or three and being stressed out. That seems kind of far away. We'll take one step at a time."

And it appears both Mary-Kate and twin sister Ashley are happily in love. Ashley also has a much older beau -- 48-year-old Foxcatcher director Bennett Miller -- who she reportedly started dating early last year.

PHOTO: Ashley Olsen's Boyfriend Is Even Older Than Mary-Kate's

But are we ready to see Mary-Kate and Ashley on the small screen again?! Last month, Netflix's chief content officer, Ted Sarandos, teased that the two are still "teetering on whether or not they'll be around" for the highly anticipated Full House reboot.

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