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French won 17 of her duels and lost the other 18 which left her with 202 points while Murray won 14 and lost 21 and therefore earned 184 points.
Murray was the silver medalist in London 2012 but she already has a mountain to climb this time around.
When Murray won her silver four years ago she ended the fencing in second so today's session will go down as a huge stumbling block for the 26-year-old from Preston.
The pair will have a chance to redeem themselves in the swimming part of the pentathlon tomorrow afternoon.
French will beat in heat five of six and Murray will be in the final heat.
Heat five will be at 16:20 and heat six will be five minutes later.
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