Take the TGV. Much nicer trip and between getting over to AF, checking (and paying for) bags, going through security and all of that and then arriving at NCE ... don't think that's worth it. But you'll have to take the RER into town and then take the TGV to Nice; there doesn't appear to be anything non-stop to Nice from Roissy right now.
LH service in Eco will be much better than UA. 1h in FRA is a bit on the tight side, although A --> Z connections are generally o.k. unless there are arrival delays. I would not worry too much about 1h40 at DEN.
Don't think LH will retire the 343 that quickly; they are just bringing 346s back from storage due to demand.