Florine is from the French and Latin flos / florem (flower, blossom) — feminine elaborated form. Saint Florine — early Christian Gaulish saint. Florine de Lorraine — medieval French princess. Florine Coomans van Brachten — Belgian historical figure.
Florine does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
In Pythagorean numerology the letters of Florine reduce to 7, The Seeker. This is a traditional interpretive system, not a factual claim about the name.