Mickael Antoine-Curier gave Hamilton the lead from close range 13 minutes before the half-time interval.
Mickael Antoine-Curier headed a reply a minute after the break, but Prince Buaben poked home after 59 minutes.
Mickael Wamen, the CGT union's representative at the Goodyear plant was more forthright.
Barthez has publicly backed Nantes keeper Mickael Landreau to win the third goalkeeping spot in Roger Lemerre's 23-man squad.
Mickael Antoine-Curier was Accies' lone striker, but he had almost no support in the opening stages as Hearts held on to possession.
Mickael Silvestre failed to clear the ball on the edge of the area and it fell to Messi, who curled home a superb equalizer.
Playing staff also laid-off included Brian Kerr, Mickael Antoine-Curier, Eric Paton, Dominic Shimmin, Njazi Kuqi, Paul McHale, Scott Fox, Colin McMenamin and Charlie Grant.
Michael Duberry and Steven Anderson kept Accies strikers Mickael Antoine-Curier and Damian Casalinuovo at bay but the visitors did manage a shot on target in the 30th minute.
Accies' top scorer Mickael Antoine-Curier made his team's starting line-up, despite concerns that a knee injury might preclude his participation, and had he not strayed offside an equaliser might well have resulted.
Paixao continued to pose a threat to United in the second half and the Portuguese player crossed invitingly for Mickael Antoine-Curier but the big striker could not direct his header on target.
Australia's Robbie McEwen won the green jersey given to the best sprinter for a third time, and Denmark's Mickael Rasmussen earned the polka-dot jersey awarded to the best climber for a second year.
Liverpool's three-pronged attack of Ryan Babel, Dirk Kuyt and Torres were moving the ball around crisply and a second goal almost arrived after a Gerrard corner, but keeper Mickael Landreau was alert to Daniel Agger's flicked header.
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