Usually, franchisers don't want to gamble on young entrepreneurs—they prefer seasoned managers who have built up lots of savings to plow into the venture. Now a host of companies are rethinking that logic. They're aggressively recruiting twentysomethings through franchise brokers, marketing themselves in youth-friendly venues like Facebook, and in some cases offering financial lures to get young people on board—such as deep discounts on franchise fees, which many beginners can't afford.