Power supply 12V 300mA
Is 400 mA more or less than 300 mA? If it's more you're operating your supply out of spec.

If the supply is from a high-quality reputable vendor, it's not likely to start a fire (but why take chances?). It is likely to fail much sooner than you'd normally expect, and the output voltage might sag noticeably.

If it's from an EBay seller or similar source with no reputation to protect, it could fail even if used close to but below the spec it was sold to you under, and it could indeed catch fire.

Note your motor probably only draws 400 mA when run with it's maximum rated torque load. If you run it with a very light load, it will draw less current, and you may be okay with the under-rated power supply (until something stalls the motor and suddenly you've let the magic smoke out of either the motor or the supply).