This will be a challenging project. For one thing, the floppy controller you mentioned doesn't include the Phase Locked Loop (PLL), so you'd have to supply that circuitry yourself.
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No matter which FDC you choose, you'll need to have a means to rapidly move the stream of bytes between memory and the FDC. In the diagram above they've addressed the issue by including a DMA controller. You could do the same, but it increases cost & complexity. The alternative is to let the CPU do it. You'd need to write a tight loop in assembler that's fast enough to move each byte in a timely fashion. (Remember you're obliged to keep up with the speed of the disk as it rotates under the head.) Single density might not be too tough but double density has double the data rate, and is probably more than an 8080 can keep up with (unless you include the DMA).
I get nostalgic thinking about floppies, but the reality is I have no desire to actually use them -- they're too small (in capacity), too slow and too failure-prone! Give it some thought. Is it possible you'd find it more rewarding to interface your 8080 to a modern, miniature SD card? It'd be a lot easier than getting a floppy working.
cheers.
Jeff