We are in talks with an enterprise to start a pilot project for our software. Is it a norm for companies to pay for a pilot project? Or should it be free to get a foot in the door and learn more about their problems and processes
Generally speaking, Yes.
I say this for a couple primary reasons.
1) If you do not place value in your product, why should the customer? And if you are not charging for it you are not placing value on it.
2) the customer will be more "invested" in the success of something that has cost them something. If it was free and it fails, "who cares"? if it cost them resources they may be more interested in making it work.
There could be overriding factors, but this is where I start with a question of this nature.