You should always (always!) have a discussion with your management months ahead of the expiration of a contract. In that meeting you can discuss:
- Whether both parties are interested in renewing the contract
- What conditions both parties want changed with the contract
- What revised rates should be applied to the contract
If you do not have this discussion, you have zero job security, and could find yourself without a contract and without a job, in a far worse position to negotiate with that company (or another company). If you do not have this discussion, the company has no guarantee that you will be willing to renew your contract or do the work within their budget.
While it would be nice if both parties were to see it in their best interests to start the negotiations early, in reality the employee is in a far worse position most of the time meaning that the employee needs to be proactive in starting that discussion.
Unfortunately, you didn't do that, and so there are a lot of questions and concerns about what will happen in the month. I'd sit down with my manager and have an honest discussion. You can start it off with something like this:
Hey boss, we've worked together for a year now, and my contract is going to expire in a month. I wanted to sit down and discuss where we want to go from here, and what's best for both of us. Is the company planning to renew my contract, either for the same job, or for another job in the company?
While I would love to think that this conversation will allow everyone to come to a mutually agreeable conclusion, the company is well within their rights to say, "Sorry, it didn't work out, we won't be renewing your contract" and you will be out of work in a month. So even prior to having that discussion with your management, make sure that you update your resume and start sending out feelers to your professional network or anywhere you would like to work if the job with this company falls through.
In the future, remember that the major merit of contracted employees to the company is that they are really easy to part ways with at the end of the contract, and that contracted employees have the least job security. It is your responsibility to manage lining up a next job at the end of your contract, or proactively discuss with the company the potential to join as a salaried employee, renew your contract, or tell the management that you are planning on looking for other opportunities in a month if you don't think it's a good fit.