Okay, I just tried playtesting Francia and Burgundy. This time, I decided to play as Francia, to see what all the sucking was about, assuming I can play better than the computer.
I think the reason they're sucking it up is a lack of starting technologies. When the Bulgarians spawn in 648, they have "Calendar, Architecture, Theology, Stirrup, Map Making, and Monasticism." Their score as of founding one city: 293. I'm playing as Francia, and I'm doing much better than Burgundy right now. My score is only 210, Burgundy is at 153. And Bulgaria has a HUGE tech advantage, nevermind the Byzantines and Arabs. My only techs as of now are Theology, Monasticism, and 5 turns shy of music. That's 545 tech points compared to 597. Doesn't sound like too much, although when you consider the limitations I had on what I could build at the startup, the reality is a little bit more debilitating. And based on what Burgundy is doing, it seems like the lack of building choices (due to lack of starting techs) leads them to mass produce units, which slows down their research, which means a lack of building choices, which means more units. It's a vicious cycle.
By turn 744, the gap had widened. Only a few turns after their start, Cordoba had: Calendar, Architecture, Theology, Manorialism, Stirrup, Engineering, Herbal Medicines, Map Making, Literature, Code of Laws, and Lateen Sails.
I had Theology, Manorialism, Monasticism, Music, and Literature. I think Lateen Sails alone is worth more than all of my techs combined.
Now Cordoba is more advanced in technologies than Spain, reflected the more advanced Moor learning. But I can see even if I focus on trying to keep up with technology and ignore aggression based expansion, I'm going to have a very difficult time. The computer AI is even worse.
Therefore, I propose both Francia and Burgundy start with Calendar, Architecture, and Theology. We can playtest that and see if it helps them stay more competitive. If they do better but still get dominated by later civs, than maybe we add a few more techs. If it doesn't make a difference, we go back to the drawing board.
Final note: if Burgundy gets two cities on the flip, I think they will dominate Francia unless Francia starts with two Settlers or at least one city on the flip. France has a slightly better starting position, but I've seen games where Burgundy did just as well under the current version.