French polish is a method of applying shellac, using a pad instead of a brush to fill the grain and build a thin film on top of the wood. Shellac itself is a resin produced by an insect that lives in trees in India and has been processed to be used as a coating. It is a non-toxic material that is soluble in alcohol.
The application of shellac can be by brush or in the case of French polish, by pad. As numerous as there are French polishers, there are as many techniques. The method I use is one I learned from reading George Frank's writings, modifying his method based on my own observations and the specific needs of the restoration. While I often modify the method on the fly to address particular issues, the one rule that I am pretty consistent about is keeping the film thin. Shellac, does not fare well in thick applications. Thick coatings are prone to cracking and alligatoring, and may not dry properly.
Shellac is essentially a solvent varnish, i.e. it dries by the solvent evaporating, leaving a hard resin behind. Another example of a solvent varnish is nitrocellulose lacquer. Both shellac and lacquer can be redissolved by wiping on the appropriate solvent—alcohol for shellac and lacquer thinner or acetone for lacquer. Shellac and lacquer films can be reconstituted by the judicious application of their solvent and the film can be reworked. This characteristic makes shellac (and lacquer) restorable. The finish does not need to be removed but can be re-amalgamated and polished again and again. Since most antiques have been finished using shellac, this technique is an invaluable tool for the restorer. By contrast, alkyd or oil varnishes "dry" by oxidation—they absorb oxygen from the air and polymerize, forming long plastic chains becoming a hard solid. These films cannot be redissolved and must be removed and a new finish reapplied.
Obviously some finishes will have become so damaged by water, sunlight or daily use, that refinishing is really the only option to restore the beauty of the wood. In these cases I refinish with shellac applied by French polish. The process is basically rubbing a pad over a surface, repeatedly, until the grain is filled and a film forms. Because there is no sanding during the process, the pad rides over and preserves the bumps and dips that we associate with old surfaces. If after a few years, the surface becomes scratched or dull, the surface is cleaned and reworked, adding a little more shellac to fill in the scratches.
Caring for a new shellac finish can be no more than dusting with a cotton cloth—no spray polishes needed. After a year, the surfaces can be waxed periodically, once a year is frequent enough. I usually avoid waxing table tops as the wax film is soft and the surface can become easily smudged, but wax will do no harm as long as it is a paste wax. I avoid spray waxes, liquid waxes and oils that can penetrate areas where there are breaks in the film. They will contaminate glue lines and stain the wood under the finish. More importantly, most liquid and aerosol polishes are a source of silicone contamination, making future restorations much more difficult.