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Defending champion McIlroy posted a one-over-par 73 to end on one over, five shots short of the cut mark.
Rank outsiders Im and Hebert both shot rounds of 67 to lie 13 under and retain the one-shot lead they held over the chasing pack after the first round.
Spaniard Jon Rahm is one behind on 12 under after also firing a 67.
Frenchman Hebert and American Im were among the early starters on Friday and registered seven birdies and six birdies respectively in their five-under-par rounds in testing wet and windy conditions.
New Zealander Ryan Fox and English duo Matthew Southgate and Oliver Fisher are well in contention on 11 under, with American Paul Peterson also challenging strongly on 10 under.
McIlroy began the tournament with a disappointing level-par round in benign conditions on Thursday and needed a bright start to Friday's second round to reignite his hopes of making the last two days.
A bogey at his first hole of the day, the par-three 10th, saw the world number four immediately drop a shot, before carding three birdies and a second bogey on the remainder of his opening nine.
The Northern Irishman picked up a shot at the fourth hole but a bogey at the sixth and a double bogey at the eighth sealed his fate as he was forced to watch playing partners Rahm and Hideki Matsuyama make their mark near the top of the leaderboard.
"I felt like I was battling well, two under through 13, and with another par five coming up, but bogey at the sixth took the wind out of my sails,"  said McIlroy, who showed his frustration by slamming his driver to the ground after a poor drive at the 16th.
"My short game, in general, it's just silly mistakes," he said. "I'm just not being very efficient with my scoring and that's why I'm making it difficult for myself. Just need to tidy up the short game a little bit; I feel like the long game is there."
The four-time major winner will compete in next week's Scottish Open before heading down to Royal Birkdale for The Open Championship.
"Obviously, I might have a few commitments here this weekend, but I need to practice," he said. "I need to get sharp and get ready for next week and ultimately for The Open in a couple week's time."
World number two Matsuyama is well placed on nine under, the same score as fellow Japanese player Hideto Tanihara, who recorded the lowest score of the day with a 65.
Paul Dunne is best placed of the Irish contingent on eight under, along with others, including Jamie Donaldson and Soren Kjeldsen, two of 11 former Irish Open winners in the field.
Major champions Padraig Harrington and Justin Rose, plus last week's French Open winner Tommy Fleetwood, are among a group still well on touch on seven under.
Among those to miss the cut was local hero Graeme McDowell, who slumped to a six at the 18th, a double bogey which proved decisive in him missing the cut as he finished two under.
The tournament forms part of the prestigious new Rolex Series of events, boasting a prize fund of £5.4 million, with £585,000 for the winner.

The 21-year-old will finalise a £31m move to Old Trafford when the transfer window opens in June.
Depay made his final appearance for PSV on Sunday, playing 83 minutes of their 3-2 victory at Den Haag.
He finished the season as Eredivisie's top scorer with 22 goals as PSV secured their first Dutch title since 2008.
Rory McIlroy missed the cut at the Irish Open for the fourth time in five years as Daniel Im and Benjamin Hebert led after day two at Portstewart.
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PSV Eindhoven winger Memphis Depay has completed a medical at Manchester United.