I do not think I have the proportions in place, I want the shoe to fit into the hand and maybe represent someone coveting it. I am not sure how to express this as a logo.
Proportions are off. A foot is larger than a hand, and therefore its shoe is larger still. This looks like an adult hand with a child's shoe floating above it. Just grab one of your shoes and hold it.. compare it to the size of your hand.
Are there any mistakes in terms of elements and composition?
If the goal is two, completely independent, non-related, static, icons, then it's there. If the goal is a single cohesive image that conveys a message, this fails miserably. There's no relation to the two images other than consistent stroke weights. It's a floating shoe with a floating hand under it. At the very least eliminating the space and actually placing the shoe in the hand would help this considerably.
Does it relate to the target audience?
Uncertain. What is the audience? There's no mention of that in your question.
What could i do to make it better match the client brief?
Create a single image, not two separate pieces floating. The hand holding a shoe is a decent concept to track, but to convey "covetous, marketplace, trade" it may be wise to rethink the imagery. All I see really expressed here is "sneaker".
"Covetous" would need some connotation of greed, desire, envy. "Marketplace" would need a connotation of purchase, acquisition, desire, shop. And "trade" could be conveyed with the same greed, desire, envy as covetous and the same acquisition as marketplace.
It's also a very static image set. "Covetous", "Marketplace", and "Trade", to me, convey some action and liveliness. Not really seeing any of that in your image.