Question

how does venous return directly influence the heart rate?

Answer 1

Venous return is the blood flowing to the heart, according to the Starling mechanism of the heart, The output of the heart is equal to and determined by the amount of blood flowing into the heart, and may be increased or decreased  within very wide limits according to the inflow of blood.

When there is increased venous return, there is greater diastolic filling of the heart, because of which the cardiac muscles are more stretched, there is more force of contraction, because of all these there is increase in stroke volume and cardiac output, and cardiac output can increase when there is increase in heart rate.

Thus with increased venous return there is increase in heart rate and vice versa.