Delta's flexible date search - the calendar - searches Delta-operated flights only. If you search by specific dates, AF and KL options should be displayed.
If you want KL or AF metal specifically, and you're starting from an AF/KL gateway at ORD, the Flying Blue award search engine is the easiest way to find Delta SkyMiles-redeemable dates. Look for Classic awards in coach or business, not premium economy or First. Punch those dates and flights in delta.com to redeem. Or just call Delta and ask for AF/KL flight options.