I'm only familiar with one domain of enterprise software and that's ERP software. I'd like to see a %age number for "vast majority" but let's just say I'm struggling to think of ERP software based on the .NET stack outside of the Microsoft products (which are not exactly a success story). SAP is based on Java/ABAP, Oracle is based on Java, Salesforce is mostly Java (and those already cover >50% of the worldwide market). I think Infor uses both Java and .NET but maybe someone else can chime in. About the only .NET shop I can think of is IFS.

Zero of the FLOSS ERPs that I know use .NET for obvious reasons (mostly Java as well, some Python and the occasional Perl etc.). Maybe some will in the future but who knows. I'd also argue that most new ERP will likely be written with a "web-first" mindset which might mean .NET but is more likely to mean more traditional web stacks (imo)

Microsoft products are certainly used all over the place (most notably SQL Server in SAP products) but I think for this sub domain Java is king. Since ERP is a decent chunk of enterprise software I don't think it's likely that a "vast majority" of enterprise software is indeed based on the .NET stack.

What data are you basing this statement on? I'm genuinely curious because the vast majority of indicators I've seen clearly show that Java is by far the #1 enterprise language. Greenfield projects are probably far more likely to choose .Net but for now, there is a hell of a lot more important legacy Java code that will never be practical to port.

I believe that C#/F# are the future of managed enterprise languages (Roslyn, CoreCLR/FX, and quite soon RyuJIT are far superior to Java equivalents, imo) but I highly doubt their adoption is anywhere near Java.