Your website (at least on root) is unproxied , CF would just serve both the A or AAAA records and let the browser deal with the rest. Browsers have different behavior but generally will try others (or race them) if one fails.
If proxied and you have Pro or higher CF has zero downtime failover to automagically try the other one: Protect your origin server
If you want something more then that/removing IPs which are failing from being served and such, you want a more full load balancer like Cloudflare’s: Cloudflare Load Balancing which can work proxied or unproxied.