I'm afraid there's no simple answer to this one... If the burn has managed to charr deep into the veneer, the best fix it is to cut out the damaged piece AFTER finding a suitable colour matched replacement to make a replacement patch. A pro french polisher should be able to create a seamless join after you've done the dirty (replaced the damaged area)..
Part 2 of the repair... the vital part..... apply the business end of a 12 gauge shotgun to the mouth/backside (del as appropriate) of the guilty party...and squeeze the trigger.... just dinna tell em its loaded with split peas....
I agree with midnight .
if you have no match for the venner I sometimes use car body filler for the patch and then paint ,and french polish to finish. only works on small repairs.but can get you out of trouble.