FixedColumns has been compatible with FixedHeader since the release of FixedColumns 4. There is an example of the 2 working together, with both header and footer, at https://datatables.net/extensions/fixedcolumns/examples/integration/fixedHeaderFooter.html
However, if you don't also use scrolling (scrollX / scrollY), the cells in the table header and footer are not fixed horizontally.
After many hours I finally figured out how to solve it with this css:
th.dtfc-fixed-left {
background-color: white;
top: 0; /* for the header */
bottom: 0; /* for the footer */
z-index: 3 !important;
}
Tested in Chrome and Firefox with FixedColumns 4.1.0 and either FixedHeader 3.1.9 or 3.2.3.
Here's a demo: http://live.datatables.net/nujapafu/1/edit
Perhaps this is something that could be incorporated in the Datatables code?