Left-handedness and Right-handedness - Are they genetic?
Handedness has, like many traits, a non zero heritability. You now should read the post Why is a heritability coefficient not an index of how “genetic” something is? to understanding what heritability mean.

In short, yes part of the variance in handedness seen in the human population is due to genetic variance.

You will note that footedness is highly correlated with handedness (wiki > footedness).

Note also that today, in the western world at least, it is generally considered unhealthy for the kid to force him/her to use its other hand (as the catholic church used to do). I am not sure what are the evidence for that but it is a totally different question.

References


McManus et al. 2013
Brandler and Parachini 2013
Harmour et al. 2014