I don't use React, so I'm not sure about your situation. However, I pass parameters in the Route() method, using named routes. I also use inertia's useForm().
So my call might look something like:
my_form.put( route( 'calls.edit', { 'param1': value1, 'param2': value2 } ) );
Inertia's useForm() is pretty helpful and route() makes the code cleaner. I don't use the method or action attributes in forms anymore. For more info, see the 'Form Helper' section in the docs:
Note the Inertia route() is slightly different than the Laravel version, because it passes the params as an object rather than an array.
Also, fwiw, I only use post, put or delete on forms.
Inertia's useForm() makes form handling fairly straightforward for most situations, and you can fall back to axios (included), if it's needed.
HTH,