I suggest you create a new table that links both those tables together. That way, you have only product information in a product table, only customer information in a customer table, and another table to determine who has what. This also will provide the many-to-many relationship you will want. For example, it's possible that a customer may have more than one product. Similarly, a product can be purchased by many customers.
[product]
product_id
product_name
product_description
[customer]
customer_id
firstname
lastname
email
[customer_product]
customer_product_id
customer_id
product_id