The names of 37 footballers, including Evelyn Lintott, a former England player and the first chairman of the Professional Footballers' Association (PFA), are also commemorated here.
Reddin, along with the squad's sports scientists, said the trip would be too draining and likely to impact on the team's performance at the tournament, according to the Times.
FA chief executive Martin Glenn will represent the FA and England at Thiepval later on Tuesday.
Midfielder James Milner and goalkeeper Joe Hart made video messages after being blocked from travelling to the memorial.
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"Among those who died were football players -- professional and amateur -- and of course football fans. Others were so badly injured they could never again play the game I love," Milner said.
England, who are in Group B, play their first match of the tournament against Russia in Marseille on Saturday. Wales and Slovakia are the other teams in the group.
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
