There is no Central Act governing the provision. You will have to consult the respective state act. This would be a very small act without much of technicalities. Presuming your organisation to be covered under the Tamil Nadu Industrial Establishments (National, festival and special holidays ) Act 1958, the provisions are as follows:
1.The employees covered under the Act shall be allowed in each calendar year a holiday of one whole day on the 26th January, the 1st May, the 15th August and the 2nd October and five other holidays each of one whole day for such festivals as is specified in this behalf by the State Government.
2. Wages. - every employee shall be paid wages for each of the holidays allowed to him .
3. Where an employee works on any holiday allowed so he shall, be entitled to either :
(a) twice the wages; or
(b) wages for such day and to avail himself of a substituted holiday with wages on one of the three days immediately before or after the day on which he so works.
So if the national holiday falls on Sunday, the employees availing the holiday will get wages for the day and those who work on that day get benefits as above.