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Recover/Carve FAT32 file system metadata (file names etc.) without partition table

I have a broken SD card, of which I’ve taken an image. The image is fairly complete, >99% according to ddrescue, and conventional data recovery tools seem to be able to find most files. However, I’d like to extract as much of the file system metadata (file names, directory structure) too.

testdisk did not manage to recover the relevant partition information. My assumption is that the SD card got formatted, only overwriting the partition table stuff while keeping the data intact.

So, how do I extract as much of the path names from this corrupt file system? I know that the partition I am interested was FAT32 formatted, and its rough size and location (thanks to entropy analysis).