In the late 1860's, there were 2 similarily-named regiments; the Scots Fusilier Guards, and the Royal Scots Fusiliers.
The first named became the Scots Guards, who are of course still part of the Guards Division, based in London. This seems the most likely regiment of your ancestor, given the timescale.
Their archives are here....
http://www.theguardsmuseum.com/Family-Research......
The other regiment was the 21st (Royal North British Fusiliers) Regiment of Foot, who became the 21st (Royal Scots Fusiliers) Regt. of Foot in 1877. The R.S.F. amalgamated with the Highland Light Infantry in 1959, becoming the Royal Highland Fusiliers.
Details of the R.H.F. museum / archives can be found here.....
http://www.rhf.org.uk/..........
Both regiments fought in the Crimea, so good posibility your ancestor could have been present.