Taiwan's La Fayette Frigate use RIM-72C/RIM-92C Sea Chaparral system for air defense.
The Ford MIM-72 Chaparral land-based air defense system used AIM-9 Sidewinder missiles and was in service until 1998, when it was replaced by the Avenger air defense system with FIM-92 Stingers.
The Naval version of the Chaparral (Sea Chaparral) was never used by the US Navy, but was exported to Taiwan. I think Taiwan is prolly one the last users for the Sea Chaparral system.
I've never seen an La Fayette equipped with Mk 41 VLS system, but the newest model can use A43 SYLVER VLS launchers for Aster-15 missiles. Note that there are 2 basic SYLVER variants, the A43 can hold missiles up to 4.3 meters in length, and the A70 can hold missiles up to 7 meters in length. There's also the enlarged A50 for land-attack cruise missiles.
I'm not sure what the length requirement for the Mk 41 VLS system is, but the La Fayette frigate might not have the space for it. This is speculation on my part and should not be considered a fact.