Old site first in organic search, if I reform it, I lose rankings?

SEO involves dozens of features such as meta tags, .htaccess, sitemap, meta keywords etc. SEO works directly with the content of these tags, and then you should redo your site as close as possible, with the same urls. Working with CMS will make the process even more difficult, you should be aware of the way this CMS handles SEO, check the plugins it provides, use the same keywords on each page. Generate site-map again and update to google database. Generate the print of the current status of your links, and then redo your site by looking at that data. You will fall into the rankings for sure, but if you do a good job, over time it will rise again. It will depend on the moment, the equal optimization between the two sites (New and Old). I do not have data to pass you, percentages or something. But we know the competition and complexity of working with SEO, and any change will surely hit your rankings.