French Cuffs without jacket, tucked into dress pants - NO!
1) It looks undressed. FC tucked into dress pants without a jacket is like wearing pants without a belt. Yes, there's nothing stopping you from doing it, but it just looks undone. Incomplete. Even on "Wall Street", Gordon Gekko wore a jacket and only took it off in the office thereby revealing FC shirt.
2) It looks like you're trying too hard. To an onlooker, the main difference between a french cuff shirt and a non-FC is the cufflinks. When you wear a FC with a jacket, you're dressing up - that's the statement you're making. You're saying to the world, "I'm dressed up." You're also hiding your cufflinks under the jacket - understated. When you wear a FC without a jacket, it looks like you're saying to the world, "The only reason why I'm wearing a FC shirt instead of a normal shirt is because I want to show off my cufflinks, to show you how expensive they are, how sophisticated I am. Look at my cufflinks." Yikes! Haven't you heard? Showiness is out. Understated is in.
French Cuffs without jacket, untucked, casual pants - YES!
1) (Caveat - I'm talking about semi-casual FC-shirts that are *made* to be untucked, not the formal pressed ones with long skirting. ) By matching FC *untucked* with *casual pants*, your statement is, "I'm deliberately breaking the rules!" In this case, your cufflinks become your fun jewelry to jazz up the outfit. Cufflinks should NOT be too formal or too expensive looking in this case. Look a little rumpled. Do not be too pressed or you'll look like you're trying too hard. ;-)
Just my two-cents from a female on-looker. Yes, of course you can wear whatever you like, or what you find comfortable. Do you like wearing your pjs? Do you wear it outside the house?