It seems to me that what you wish is a Personal Information Manager (PIM), and I assume that when you say "synchronization with external device" you mean with an Android or iOS mobile phone (I am not considering you use palmOS PDA or anything similar).
For this I would suggest you look at EssentialPIM: https://www.essentialpim.com/
There is a free version for you to try (not demo-time limited, free forever with less features than Pro version). The free version syncs with mobile phones.
It will be difficult to find a PIM that is not "email-centered" though.
It would also be good to look at "Business Card" apps - the ones that Scan business cards and automatically generates a contact card. Most of them integrate with your phone address book, however there are a few that allow for the contacts to be kept separately from your address book (in the app itself). I use CamCard for instance.
There are other approaches to this: use of database applications, like Symphytum (http://giowck.github.io/symphytum/) where you can create contact form and be able to edit this form however you wish (some contacts have emails, some do not).
Open source software for PIM nowadays is difficult to find, as they are mostly self-hosted CRM solutions, which I believe is not what you are looking for(a more end-user scenario).
In any case I believe EssentialPIM is your best choice, not Open Source but a free version and if you like it, you can just buy it and not have to subscribe to anything.
I hope I helped. Cheers.
