[Note: I am sticking with the masculine terms throughout this post; everything applies equally to the parallel feminine terms.]
Some will tell you there is a ‘correct’ way. They are wrong. Both ‘Great Uncle” and “Grand Uncle” date back at least to the 15th century. (see citations below)
- “his grete Uncle H. Cardinal of England” (Rolls of Parliament V.438, 1438)
- “his graunt oncle Henry cardinalle of Englande” (Book of Noblesse, 1475)
Great derives from the Germanic ’Great.’
In French, the construction is very logical for uncles, fathers, and sons
- Great Grandfather
- Great Grandson
- Grand Uncle
- Great Grand Uncle
- Grand Nephew
- Great Grand Nephew
Some like a construction similar to the French, but using Great.
- Great Uncle
- Great Great Uncle
Personally, I like the French system.