How do I keep my French knots from turning into lumpy blobs?

The flat vs fat knot thing usally comes down to how you cinch the wrap, not how many wraps you use. Two wraps for most normal floss, three if you're working with a single strand and want them chunkier. The trick is that the wraps have to stay snug against the needle while you take it back down, then you hold that little bundle with your thumb until the tail comes through. If the wraps slip or loosen even a bit while you're pulling the needle through, you get a lazy knot that sits flat. Also pull the needle through slowly. Yanking it fast lets the wrap slide off shape before it seats against the fabric.

Not much to add on the knots yet since I'm still figuring those out myself, but the wavy fabric thing I know from doing text with lots of close stitches. Mine puckered badly until someone suggested I loosen the hoop a little once the area fills in, and to work from the middle of an area outward instead of edge to edge. Also, pressing it face down on a towel with a damp cloth afterward flattened mine out quite a bit, though the knots might behave differently than my satin stitches did. Does anyone here block hoop projects after finishing, or would that mess up raised stitches like French knots? Still figuring out what's normal on this forum.

Gotta push back on the slow pull advice. I pull fast and my knots come out even, so I don't think speed has anything to do with it. What actually fixed my flat knots was the exit hole. If you go back down even a hair away from where you came up, the wraps slide down the needle and the knot never puffs up. Dead same hole, every time, and suddenly they're all fat. For the puckering, I'd say stop chasing perfect hoop tension and just accept that dense knot areas always wave a bit. Press it at the very end and it mostly settles.

One thing that made a big difference for my knots was stripping the floss, so I was using two strands that weren't all twisted togehter. When the strands twist up mid-knot the wrap gets lumpy and some come out fat and some come out skinny no matter what my hands are doing. I let the needle dangle and untwist every few knots now. For the puckering, I stitch dense fills on fabric with a scrap of muslin basted behind it. The knots have somethig to grab into and the ground fabric stays flat. Tried it on a piece with a big knot-filled hill after puckering the first attempt, and the difference was night and day.

Agree with the stripped floss tip, that fixed half my uneven knots too. The other half for me was switching to a milliners needle. The shaft is the same thickness all the way down so the wraps slide off clean instead of catching on a fat spot near the eye like they did with my regular needle. I keep one just for knots now, sounds fussy but it genuinely made them all come out the same size.