If there is a clear and good explanation of why she needs the visa fast, it will be possible to get it in short time.
As Greece is a tourist country, they will not pull up big barriers provided that she meets the basic conditions.
With a Schengen visa for all the area (C), you do not need transit visa if you enter the area in another country. The visa should be applied for in (A) the country of destination or (B) the country of entry in to Schengen territory. There for not only the Greek consulate but also the French consulate could be asked.