The image above shows how using your feet in beach volleyball happens throughout play. The player above thinks using his feet is the best way to keep the ball alive and in play, so he is attempting to kick the volleyball up.
Yes, you are allowed to use your feet in both women's and men's beach volleyball!
While you are allowed to use your feet in both indoor volleyball and in beach volleyball, the rules haven't always been that way. Using your feet to make contact with a volleyball used to be illegal. Now it is perfectly legal. You are allowed to use any part of your body to make contact with a volleyball, and the ball will remain in play. When a player hits a volleyball with their foot, it counts as one of their team's three hits, and the play goes on.
A player will typically attempt to use their foot to hit the volleyball if they think it is their best chance at keeping the ball in air and in play, hitting near another teammate or back over the net. We usually see foot hits after a spike from the opposing team. This is when using a foot hit tends to work the best, as a dig, to counterplay a spike.
Using your feet in beach volleyball is allowed, but it is also rare. Still, when it does happen it's an exciting part of the game. Infact, there is a sport called soccer volleyball that only permits players to use their feet and legs. This is usually played on a beach as well, with a soccer ball.