That's just like how C# and VB.Net can co-exist in the same project. Would you pick the pattern of:
1: C# Library with interfaces and/or abstract base classes
2: F# library with implementations of those interfaces and base classes
3: C# program (console, web service, GUI, ect) that specifies the implementations in Dependency Injection
Or is there a simpler way for C# and F# to co-exist in the same project (dll or exe)?
F# excels in writing domain logic where main domain entities are defined as records and discriminated unions and logic is written in pure functions. Given that product is preexisting and domain entities must already be defined, I wonder what use case do you have in mind?
Realtime control logic for infrastructure.
The basic decision making logic needs to be very simple and easy to follow by scientists and people who aren't day-to-day software engineers: Basically, input some data, such as sensor readings, run it through an algorithm that makes decisions, and then output the decisions.
You don't really need to split 1 & 2, since F# can define .NET interfaces and abstract classes just fine.
For that matter, you don't even need the interfaces if you wouldn't have had them in a C#-only solution. Just define the class in F# and use it directly from C#.
You still need a separate assembly for F#, but that doesn't imply dependency injection - again, just reference it and use it.