I just took my first batch of french breakfast radishes out of the ground!!! I am wondering if it is too late to put another batch in? (they are cool weather crop, right?)
Yes it is too late to plant more radishes. They are a cool-seaon crop. While they will grow for a while in hot weather, their flavor will be unbearably strong.
In late winter/early spring, you can start planting radishes as soon as your soil temperature at planting depth is 45 degrees or highly...so probably in late January or early February of an average year. You can succession plant more whenever you choose until about a month before your daytime high temps begin regularly exceeding 80 degrees. If you sow any later than that, the radishes usually are pithy and have an unpleasantly strong flavor. Also, the type of radishes we grow in late winter/early spring are annuals so high temperatures and late spring's/early summer's longer daylength causes them to flower and go to seed.
To plant radishes for fall, you can sow seed only after your daily high temps are falling below 80 degrees. For me, I think that is usually in October sometime....and not necessarily early in October and sometimes not until early November. They'll grow and do OK until nighttime lows start dropping below 40 degrees but the ones that are growing/developing once the nights are below 55 degrees will develop very slowly and sometimes can develop an odd sort of off-flavor.
You also can plant winter radishes (thery're a different type from summer radishes, and I think Dorothy grows them) about the same time you plant your fall crop of summer radishes. However, the winter radishes are cold hardy and will grow through the winter for harvest in winter or spring. Usually winter radishes are larger than summer radishes.
I planted two winter radishes and my fav spring radish French Breakfast last fall. The winter were Daikon, a long big white icycle type and a small round green and rose one from Baker's. Forgot the name. Neither of the winters actually overwintered, but froze out in midwinter. The only thing that reliably overwinters for me here is spinach and this last winter mine survived being eaten by deer twice and zero temps. Ate the last of it this past spring very early.