When we first started to work on Replicant, we were looking for a free market replacement app for Android in order to create a Replicant Software Center. Replicant Software Center was to be a fully free software market application to download and manage free software apps on Replicant.
You can still build these apps: see FLOSSDispenserBuild and SlideMeBuild.
We are now using FDroid client. It comes with the latest Replicant images. If you want to install it manually, you can download a compiled libre apk here: http://f-droid.org/FDroid.apk
By default, FDroid downloads libre apps from its own repository. We are working together with our friend Ciaran, the main FDroid developer, to perhaps establish a Replicant repository in the future.
The applications on the list of all known Free Software applications for the Android platform should be incorporated into that.