CE marking is an administrative marking that indicates conformity with health, safety, and environmental protection standards for products sold within the European Economic Area.
The CE mark is mandatory for 'machinery and equipment', irrespective of individual components being CE or FCC certified.
The CNC product would definitely fall under this category.
Applicable directives would be 'Machinery Directive', 'Low Voltage Directive' and 'EMC directive'.
In order to meet CE Marking requirements the CNC product would need to comply with all relevant CE standards.
All electrical equipment and controls on the machine would be required to comply with EN 60204-1 'Safety of Machinery: Electrical Equipment of Machines'. The safeguards, tooling / fixturing, software and documentation would also need to be covered. This is to ensure that the safety of people using the machine would be guaranteed, the control responses of the machine would be consistent, and the machine would be easy to maintain throughout its lifetime.
A risk assessment would also be required to be performed as per the requirements of ISO 12100 (2010) 'Safety of machinery - General principles for design - risk assessment and risk reduction'.
For a start, it would be advisable for key personnel to attend a training programme on CE marking. Secondly, availing the services of a certifying agency and involvement of key personnel would go a long way in achieving 'self-certification' in the long term.