Here you see the LPD entry for niche. My poll shows that the French-style pronunciation is now overwhelmingly preferred in BrE, while (as far as I know) remaining virtually unknown in AmE.
The OED comments
N.E.D. (1907) gives only the pronunciation (nitʃ) /nɪtʃ/ and the pronunciation /niːʃ/ is apparently not recorded before this date. H. Michaelis & D. Jones Phonetic Dict. Eng. Lang. (1913), and all editions of D. Jones Eng. Pronouncing Dict. up to and including the fourteenth edition (1977) give /nɪtʃ/ as the typical pronunciation and /niːʃ/ as an alternative pronunciation. The fifteenth edition (1991) gives /niːʃ/ in British English and /nɪtʃ/ in U.S. English.So it’s BrE that’s done the innovating here.
In one of my talks about pronunciation preference polls I show three slides to illustrate the point that the evidence is that — contrary to what many people suppose — in some cases change spreads from AmE to BrE,in other cases from BrE to AmE,while occasionally we find that both are moving in tandem.
(Sorry about the Comic Sans. This is a very old talk. I’ve moved on typographically since then.)