If bitcoin gets on the mainstream then paper money will loose its popularity and users too, as if bitcoin gets widely used and accepted then people will prefer to use bitcoin more in compare to paper money as it will give them freedom of going for shopping cashless and things will become more easier.
Storage, production and the material itself is very expensive for the production of paper money. And if the popular will cryptocurrency, then paper money will be bid farewell ,.
Till paper money has support from the Government I don't think it will face any issue and we cannot expect that each and every person will start using bitcoins in future and bitcoin will always be treated as an secondary currency to paper money, and fiat will keep on enjoying its monopoly even in future.