Cleaning cotton velour stage curtains can be tricky. The biggest issue is flame retardancy. Cotton velours are topically treated for flame retardancy with a water-soluble chemical. This means that, if the fabric is washed, the drape will no longer be flame retardant (requiring costly re-treatment). Periodic maintenance, along with dry-cleaning only when absolutely necessary, will keep your drapes looking great for years to come.
Dust accumulation and repeated dry-cleaning can damage drapery. I recommend removing the dust using a soft brush, first on the back of the drape and then on the front (detailed instructions are here).
Cotton velour drapes must be professionally dry-cleaned. Small drapes may be taken to any good dry-cleaner. For larger drapes, I suggest checking with the Executive Housekeeper of a large hotel / resort in your area to get a recommendation of a good commercial cleaner. Request the use of 100% pure solvents under easy care conditions. Spot-cleaning by a dry-cleaner is also an option but may affect the appearance of the drape.
Keep in mind, however, that even dry cleaning will eventually cause your drapery to loss its flame retardancy. I recommend that you have your drapery tested annually, and have them professionally re-treated for flame retardancy as needed.