Meet the puppy on their level. If possible, spend time on the floor with them. Whatever favorable response the puppy gives you such as returning when you call his name, praise profusely. Pay attention to the pitch and tone of your voice. Although your puppy may not understand the word 'good' they are already hardwired to understand tonal inflection. This means that if you sound happy (with a high pitched tone), they will understand it to be happy. A low tone compared to the momma dog's low growl of correction.
The Coton is a great runner (agility), walker, licker, swimmer, loves people, parks, riding in the car and shopping carts, shopping centers, etc. Take your Coton everywhere. They are not “designed” to live isolated in your house 24 hours a day. Mine love visiting hospitals, nursing homes, and rehab centers. Especially my registered therapy dog, Hannah.
Cotons are people-loving dogs, they want to please you. This is very important to keep in mind as you train them. Positive reinforcement is the best method of trianing. Cotons do not respond well to 'discipline' or 'fear' based training. Instead look into treat-training for your dog. Many pet shops, personal trainers, and even professional animal trainers employ this method of training. You will find the Coton is a fast learner and will quickly 'decide' how to best make you happy. Also, the Coton is not known to be selective when it comes to socialization. They enjoy attention from children, elderly people, other dogs, cats and sometimes even lizards and birds!