You could use capture groups, its not clear if you can rely on the formatting of your data.
sed -r 's/(^.*FONT FACE[^>]*>)([^<]*)([^>]*)(.*$)/\2/' <<< '<FONT FACE="Monospace,Courier">ABCD 050920Z 31004KT 9999 SCT026 22/14 Q1008</FONT><BR>'
This puts the text you are looking for into the second capture group and replaces the string with only the second capture group (\2).