DO-178 / ED-12C
Any software that executes on installed hardware in a type certified aircraft will need go to through DO-178C (or a similar process). The amount of effort involved depends on the safety criticality of the software functions.
Since this sounds like a new system without predefined System Requirements (such as those you would get from an OEM as part of the SAE ARP 4754A processes), those will need to be defined by your development process and then your Software (High Level) Requirements trace from those.
Here in the US, smaller companies will typically contact and work with the local ACO (Aircraft Certification Office) during the product planning stages to identify the product as following the DO-178C processes.
Larger companies, especially OEMs, tend to work with DERs (Designated Engineering Representatives) rather than directly with the ACO, as they may have dozens of different DO-178 projects going at one time.
EASA Software Certification
Guidance on the EASA Software Aspects of Certification can be found in EASA CM -SWCEH - 002 PDF
From that document, Panel 10 seems to be the part of EASA that you would work with, although I haven't found how a new applicant would go about contacting them yet.
The EASA panel in charge of software and AEH aspects of certification.
This panel includes at least one software and AEH expert (who is the
coordinator) and, depending on the size of the project, may include
additional software and AEH experts.
There is also a FAQ page for the application processes with EASA: