To sit in someone’s shade means you enjoy their protection. She relishes the safety he gives her in their relationship.
She also delights in his fruit that is sweet to her taste. This seems to be a very sensual image and no doubt speaks to how much intimacy with him delights her. Her comparison certainly speaks of physical intimacy, but it is not limited to a sexual relationship–it goes beyond that, to the security she feels because of his love.1 It speaks of both protection and pleasure.2
3 Comme un pommier au milieu des arbres de la forêt, Tel est mon bien-aimé parmi les jeunes hommes. J'ai désiré m'asseoir à son ombre, Et son fruit est doux à mon palais.