The friction coefficient between plank and floor is $\mu$. The man applies, the maximum possible force on the string and the system remains at rest. Then, 

For man and plank as a system

$$\begin{gathered} T+N=2mg\Rightarrow N=2m-T \\ T=\mu N=\mu \left(2mg-T\right)\Rightarrow T=\frac{2\mu mg}{1+\mu } \end{gathered}$$

Force friction $=\mu N=T$

No horizontal force acts on man, so no friction force will act on man. Also he is equilibrium so net force acting on man is zero