Foul ball - runner has to re-touch

[WeekendRef]

With a runner on 1st batter hits a foul ball . Does the runner on 1st have to re-touch first base before the next pitch ?
From what I remember the umpire should not put the ball back in play until the runner has re-touched 1st ....is this correct ?
If it is correct let's say the runner does not re-touch after a foul ball (and the ump signals to play ball) and on the next pitch the batter hits a gapper which scores the runner from first . Is there any way the defensive team can appeal and the runner be called out for not re-touching after a foul ball ?
I am not sure I totally understand the logic behind re-touching 1st but I am not questioning the logic just curious about being able to appeal.....