The Deutsche Bahn has an offer they call "Europa Spezial" and they offer it to all neighboring countries. The interesting thing about this offer is that the price depends on how far in advance you book, and where in Germany you leave from, but that how far you travel in to the country of destination does not matter. So if you decide to use this offer breaking the journey abroad and continuing on a domestic ticket isn't really the best option. However for France DB only offers this on trains that originate in Germany. This is not a problem here.
The cheapest I see for a "Europe Spezial Frankreich" for Bremen - Lyon is 39,.- euro. This is when booked near the booking horizon. I used September 4th as a test date, and got this price for a solution involving 2 changes, a trip duration of a bit over 10 hours, and travel all in IC, ICE or TGV. That would be my choice.
If you book closer to your date of travel prices go up, but are still often a good deal.
What is also a very good deal with the DB Europa Spezial is traveling in first class. The 2nd class specials sell out faster than the 1st class. That means that often the price difference between both is not that big. For example, looking at Aug. 20th I see a 2nd class price of 79,- and a first class offer of 89,-. For me spending 10 hours in first class as opposed to 2nd class would certainly be worth the extra 10 euros...
So in conclusion I think that best value option for ground transport would be train, booked on www.bahn.de, as much in advance as possible. You can book this up to three months in advance.