The College Board recently published concordance tables for comparing new SAT scores to old SAT scores. According to the tables, a 1260 on the new SAT is equivalent to a 1760 on the old SAT, so you've improved the equivalent of around 110 points on the old SAT or 60 points on the new SAT.
On the FSU admissions website, it says the middle 50 percent of applicants in 2015 had total SAT scores of 1750-1960 points. Based on your new SAT score, you're just within the average range. If you take the SAT again, I'd recommend aiming for a 1350 or higher to ensure that you're in a really good place to apply.
UF is a little tougher because their average old SAT score for admitted students was a 1918. At UF, a 1350 would still put you slightly below average (it's the equivalent of a 1900 according to the concordance tables). If you want to have a strong chance there, you should aim for a score in the 1400s.