A French Fold is any sheet of paper folded twice, each time halving the finished size. The folds are always at right angles ~ to each other ~ to the edges of the paper ~ parallel to the sides of the paper ~ oprthogonally ~ hence another term 'twin-right-angle-fold'.
The resulting shape [107648] of the sheet is preserved by the second fold. In the 'ISO A' [122440] and ISO 'B' [122441] series the shape of the sheets is also preserved after a single fold. This makes them the popular series amongst users in many trades throughout the World.
These are usuall too inconsequential to mention, but I feel they need to be considered, and possibly overcome or avoided.
Folding a sheet of any material puts a strain on it, depending on the thickness and properties of the material. For normal office paper the strain does not nitce after the first fold. On thicker papers the strain is greater. Although hardly noticeable after the first fold it can sometimes be seen after the second fold, since a double thicknes of material is being folded.
The strain is caused either by the compression of the sheet on the inside of the fold, or its expansion on the outside (or both). The compression leads to buckling and bunching-up of material. The extension can lead to tearing. With machine-made papers ~ and other materials where the grain is pronounced ~ the paper may well tear along the grain, whereas it might not do so under the same tension but with the grain in the opposite direction. Bookbinders are aware of all this and allow for it ~ or make life difficult for themselves or their users.