According to the offical figures, there are 337 Tabathas in France, none born before the change in the law in 1993, and 84 Tabithas.
La Bible du semeur, a new translation published in 1992, revised in 2015, gives the name as Tabitha, as does La Bible Segond 21, "revised for the 21st century using modern vocabulary" (my translation of the description), published in 2007.
So Tabatha may be the preferred spelling in the last 25 years, but the Biblical spelling is still Tabitha.
And to get back to the point about Tabatha being a different name, it isn't. The website vitaminC gives a link to say:
"Histoire de Tabatha
Chrétienne vivant en Palestine, Tabitha se dévoue au soulagement des pauvres lorsqu'elle tombe malade et meurt."
"History of Tabatha
A Christian living in Palestine, Tabitha devotes herself to the relief of the poor when she falls ill and dies."