the name Maéva was used before 1970, even if very seldom: in 1960 4 girls and in 1961 5 girls were born in France
with this name.
The reason of the popularity is related with the sounds and not with the meaning. In France
, since the 80s the vocalic groups have been growing in popularity: ea (Léa), eo (Téo), ae (Maël), ai (Maïlis)...
Maéva sounds similar to other names, as Maëlle/Maëla, Maë, Maëlys/Maëlis/Maylis and Maïwenn; since some of these names are Breton, it is not unusual at all to found people (in boards) saying that Maéva is Breton, too. And that can be another reason of its popularity, because the Breton names are a trend (just as the Irish names in the US).