J'ai Obtenu Cette is a rough French translation for "I've Got This"
"J'ai Obtenu Cette" is an incomplete sentence in French. While the individual words mean "I", "obtained". and "this", the phrasing means "I obtained the". "Cette", in grammar terms, is a definite article, meaning it refers to a specific noun, which in this case, is missing. Without a noun, this sentence means nothing, like saying "I obtained the", the what.
Gemma makes a joke about being at the hospital for in-vitro counseling. When she guest starred on Shameless (2011)"Shameless", she played a woman who has in-vitro fertilization.