Are you in the UK or US?

The procedure with making CDs is to obtain a licence from the mechanical copyright rights organisation for your country. In the UK this is MCPS. You submit a list of all the tracks (including public domain ones) and they calculate a royalty fee for all those which are copyright. When you've paid MCPS they then issue a licence, which the CD manufacturer will need before they will press the CDs. MCPS is responsible for apportioning the fee between the all the rights holders and paying them.

I'm not sure how this works in the US where I believe there may be more than one licensing organisation. I'm sure someone there can point you in the right direction. I believe the rights organisations in different countries have reciprocal arrangements to ensure that the rights owners get paid.

The system is intended to avoid the problem of identifying, tracking down and negotiating with all the rights holders whom you may wish to record. However many folk composers are not professionals and may not be registered with a rights organisation. or for whatever reason the rights organisation might not be able to licence it, in which case you will need to negotiate direct with the rights holder. However this seems very unlikely to apply in this case, where the composer is an internationally-known artist.