I don’t think you are doing something wrong. Your code seems to work. When you output your variable, try wrapping it in tags <pre></pre>for testing purposes. If you want the linebreak to appear on the html page, you need to replace the space with <br />.
This works for me and shows carriagereturn / linefeed:
<cfset myVar="The quick brown fox">
<cfset myPosition = find(" ", myVar)>
<cfset lineBreak = Chr(13) & Chr(10)>
<cfset myVar = insert(lineBreak, myVar, myPosition)>
<cfoutput>
<pre>#myVar#</pre>
</cfoutput>
BTW: #, .