No. Proxychains only intercepts network connections and does SOCKS5 handshakes, and that is all.
To achieve what you said requires chaging of TLS handshake process, which is the payload of the TCP connection. See mitmproxy or my modified tcpproxy, but I won't guide you how to use them.
I have a client that only supports TLS 1.2 and old cipher suites.
I need to get a client to open modern websites.
Is it possible for proxychains to connect to my local proxy via TLS 1.3 and modern cipher suites?