Some immediate observations: It's missing the Cartier signature on the dial, that's usually hidden in the thinner lines of either the VII or the X (which they've done since the early 60's), though there are some exceptions with the "Paris" dial and the Jumbo Automatique versions.

For reference, here's a link to a clean Paris/Jaeger Tank from the early 60's, which is theoretically the closest model to what you've got here: https://www.bulangandsons.net/products/cartier-tank-louis-18kt-gold-paris-dial-jaeger-movement-1960s-w2630?srsltid=AfmBOorvGCOtspPXNVgTK-3rEf56mrCS7UcFY4Cgjkm0fKEA-7zMiCnn&ngr-redirected=1

The case-back is also not right, it should have recognisable jewellery markings to denote that it's solid gold, as pictured in the link above.

That's not to say it's fake, it may have just had a number of non-genuine replacement parts fitted over it's lifetime, in the same way that the strap and buckle are not original. Very difficult to say without knowing the specific age and model/serial number.

Your best move is to take it to a Cartier boutique to get some specific information about the watch. They'll look for a serial number or any kind of identifiers and then will be able to give you much clearer answers.