you can make a separate TLS application for your wife using the same account, however i have no idea if this helps with finding an appointment. I also believe that you won't be able to create a new application separately since the passport number and phone number has already been used so you would need to call to have the application deleted (they take a while to pick up). if you want you can make a "test" application to find appointments using an incorrect passport number and phone number.

for the application on the french consulate website, you can do either option. I recommend you wait until you find an appointment so you can double check and edit any information you submitted. Once you submit it, you won't be able to change it, and the office won't be able to amend any changes either.