The FREMM weighs about 6,000+ tonnes, so you’re technically going into destroyer territory, not to mention extra cost.
It’s kind of weird that the USN or shipbuilders didn’t think of an upgrade to the Oliver Hazard Perry class.
The Russians upgraded the basic hull of the Krivak class, older than the Perrys, and now offers variants with upgraded propulsion, some stealth features, vertically launched SAMs and SSMs. Already in service with India and Russia.