"The company decided to downsize, that's why I researched your company and found this position I believe I am qualified for."
Keep it brief the reason you are gone, and come back into with showing interest in the company.
Keep it simple and short. You shouldn't have to write an essay on why you are unemployed.
This. While I'm a fan of honesty, I think there's no reason to advertise that you were fired for 'performance' reasons. Unless you've got some super-esoteric skill that makes you a shoo-in for this job, I would say that having been fired from your last job would almost immediately disqualify you for a competitive position, particularly in this job market.