Read (repair) data from broken floppy disc on a linux system

How can I read an old floppy disk under Linux that has some problematic sectors? In times of DOS people used magic tools like Norton Disk Doctor and others.

Some of these tools read the broken part many times until they had success. Others used more intelligence. As far I remember some of these tools could repair nearly every broken file after some time.

I tried dd if=/dev/fd0 of=001.img but it stops with an error message dd_rescue continues the job, but the image is not readable afterwards.

How can I recover the files from a very old floppy with Linux tools?

Summary for the other readers

Thanks to @ChrisF and @week it worked very well in the following order:

dd_rescue /dev/fd0 data.img
testdisk data.img

I could restore even deleted files. Screenshots can be found here cgsecurity.org Finally I found another tool called (gnu)ddrescue and a discussion about the differences.

testdisk should help with this. It's an opensource multiplatform data recovery software.