There's a lot of confusion over the significance of the Nungesser/Coli flight. L'Oiseau Blanc is, in my opinion, history's most important missing aircraft - far more important than Earhart's Electra - but not for the reasons most people think. Nungesser and Coli probably did succeed in crossing the Atlantic. The evidence that they got as far as Newfoundland is very strong, but the Atlantic had been crossed by air many times before. Alcock and Brown did it first in 1919. What Nungesser and Coli were trying to do, and what Lindbergh succeeded in doing, was win the $25,000 Ortieg Prize for the first nonstop flight between New York and Paris, in either direction. Wherever N and C ended up, their flight was not a success and did not set any kind of record.
The historical significance of the White Bird is that, if it had arrived in New York as everyone including Lindbergh was quite sure it would, Lindbergh would not have flown the Atlantic and everything that happened because he did would have happened differently.