Depends a lot on his current size.
A good way to guess the size of a small round bodied fish to compare the body size to an egg.
A USDA graded small size egg averages about 42 grams,
Medium is about 50, Large is about 57, Very large is about 64 Grams and jumbo is around 71.
https://en.m.wikipedia.org/wiki/Chicken_egg_sizes
Personally I would give a small egg size fish of this shape no less than 8.5 gallons to itself, a medium 9.5, a Large 10.5, extra large 11.5, and no less than 12.5 gallons
each for a jumbo egg size Fantail.
When you do upgrade, keep in mind that front to back width is more important than length to fancy goldfish, because while they can't swim very fast, they are also very bad at turning compared to other fish.
In the end, I would suggest nothing less than a 40 gallon breeder (36"X18" base) tank for one double tail by itself permanently , with a 75 (48"X18") being a much better choice for two at most with no other tank mates, as they can easily reach a body the size a nerf American football, and not uncommonly get significantly larger.
This is really the absolute minimum, and if you can go bigger than this, I certainly would, and not getting a tank any less than 16" front to back.
PS: IF his body is already bigger than an extra large egg, he needs an upgrade as soon as humanly possible.
Edit: As a note for anyone reading this in the future, shibunkin, comet, common, and other single tail goldfish are more active swimmers and really do better with at least a five foot tank, preferably 6 feet.