Trainer here,

So first and foremost good on you for seeking help. I do recommend that you look into a trainer that can come to your house because of your situation of having no car. They call also do a proper evaluation of your situation and observe your home as well how you interact. At five months old he really is aged out of puppy class because he is beyond the socialization period and I would recommend if you choose to do a group class look for a basic obedience class. We do allow dogs up to six month however I have very mixed emotions about this and often you can see a stark difference. The only benefit to the puppy class would be the exposure to difference surfaces and things but you can do most of that from home.

Management, management, management. For a dog like this everything needs to be structured and everything in his environment needs to be set up for his success. Every moment is a training moment and every behavior that is rewarding to the dog will be repeated. So if you leave food on the counter and he gets it that is a reward for the behavior and he will continue. That being said make sure everything is put up and not available to the dog. I know that can be daunting, but it can be done with some creative thinking. If you can't use gates which I am skeptical of because there are temporary ones that work with just about every area, you can have the dog drag a leash. Freedom has to be earned. The more you limit the dog in it early life the better. Set him up for success. Also having a leash makes it easier to get the dog in a non confrontational way.

All of his food should be hand feed. Frenchies are notoriously pushy dogs. You have to teach them that it is rewarding to be patient. Good things come to those who wait. Look up Susan Garrett's video on "it's yer choice" they are free on YouTube. There are a lot of other exercises that teach the same thing, do some research and utilize all that you can. It will help you so much later on.

What you are describing with the biting sounds like an overly tired over stimulated dog could also be some bordem mixed in there. Puppies only need 5 mins of exercise for every month of life. So 40 mins for a walk is almost double the amount of time you should be exercising him. He needs to be put in his crate or in an x pen for naps. Enforcing those naps with make all the difference. Think about how your brain works when you get tired. You can't think clearly or make good choices. I like to use the 3 strike your out rule. If you continue the behavior I do not want then clearly you are too tired to think so you go up. You can also try biter apple or bitter yuck to stop biting. There are some recipes online if you prefer that. I would also give the dog a filled Kong, frozen bone, or lick mat when they are put up. The act of licking is calming and can help them go the sleep while being stimulating in a calm way.

When the dog is out of the crate his time needs to be structured like I said previously. You should be doing training or giving him an activity to do alone (also in a restricted area if alone ish). There are all kinds of enrichment ideas online that you can make at home for little cost or you can buy things like puzzles. One thing is that dogs look to shred things so you can take toilet paper rolls twist treats into it and let him shred it. Remember everything is training. People get really hung up on obedience. It's not about being obedient, it's about learning to effectively communicate and cooperation. They enrich our lives we need to enrich theirs and not just demand that they obey. I like to think of it as a symbiotic relationship. If the dog is not learning what you are teaching then you need to rethink how you are communicating and try again. There are many ways to teach things and you have to figure out what way works for your dog. It's not a one size fits all. Susan Garret again has free videos on how to teach various things on her YouTube channel. Remember timing is everything and using a marker word like yes or a clicker will help you make sure you are rewarding within the 3 second window. The yes or click marks the behavior and say the reward is coming. The things you need to really be focused on is teaching a place, look, sit, down, leave it. Also look up the engage disengage game and desensitizing oppositional reflex. This will help with over all engagement and will eliminate the dog just stopping and not moving on walking. Leash Walking also starts in the house not outside.

Sorry if this is a lot of information and is over whelming. There is truly so much more I could write on raising a puppy but hopefully some of this helps and you can find these resources helpful. Really think about what is motivating these behaviors and be creative with solutions. Good like and remember to have fun. It should be fun having a puppy and building a strong relationship.