You are right - it is best to avoid putting any cologne on your baby's skin. Babies have very sensitive skin and are more likely to suffer from an allergic reaction than an adult. Putting any form of perfumed toiletry product on your baby's skin also unfortunately makes it more likely that they will suffer from eczema.
Another worry with this form of product is the long term harm the chemicals could cause to our children. Have a look at this information on the campaign for safe cosmetics website.