First off, anytime you need a file from Microsoft, use "redistributable" as part of your search. Unfortunately, most sites do not specify 32 bit or 64 bit so you may have to give them a try to find out. The file name is often a dead giveaway though. Also, even if Windows ME is not listed, the file may still work just fine. It's just that from what I can tell, websites aren't always going that far back on compatibility info.
Found these:
Major Geeks https://www.majorgeeks.com/files/details/microsoft_net_framework_redistributable_11.html
Supported operating systems: Windows 2000, Windows Server 2003, Windows Server 2008, Windows Vista, Windows XP
Microsoft .NET Framework Redistributable 1.1 installed on Windows 10 64-bit. It should work on all 64-bit operating systems.
OldVersion: http://www.oldversion.com/windows/net-framework-1-1
Works on: Windows 98 / Windows ME / Windows 2000 / Windows XP / Windows Vista / Windows Server 2003 / Windows Server 2008 / Windows 7 / Windows Server 2012
Built-in support for mobile ASP.NET controls. Previously available as an add-on for .NET Framework, now part of the framework.
Security changes - enable Windows Forms assemblies to execute in a semi-trusted manner from the Internet, and enable Code Access Security in ASP.NET applications.
Built-in support for ODBC and Oracle databases. Previously available as an add-on for .NET Framework 1.0, now part of the framework.
.NET Compact Framework - a version of the .NET Framework for small devices.
Internet Protocol version 6 (IPv6) support.
Numerous API changes.
Source: Wikipedia
C|Net: https://download.cnet.com/microsoft-net-framework-1-1-service-pack-1/3000-10250_4-10725942.html
Microsoft .NET Framework 1.1 Service Pack 1
Operating System: Windows Vista, Windows 2003, Windows 2000, Windows 10, Windows XP
Note: .NET Framework 1.1 Service Pack 1 provides better support for Windows XP Service Pack 2 and includes other enhancements