It is possible because as a general rule, these institutions have dogs of all sorts of breeds, sizes and personalities. Go take a tour of the kennel area and when you find the baby you are interested in adopting write down the ID number, take a photo of him/her and record a video if you can. Take this information to a worker, fill out the application and when your baby is sterilized, microchipped, licensed and vaccinated you will be allowed to take him/her home with you. Good luck!
If it's a specific breed you're after then rescues may not be your best option. That being said maybe seeing the dogs and their personalities might help you change your mind about a specific breed.
As far I know no but please check with them they might have franch bulldog for you to adopt
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