There are multiple causes for this error (app crashing on launch and error 0x80073CF6 when trying to reinstall the app.)
In my case, the error was affecting the Mail and Sway apps. In my case, the error was caused by adding support for non-US keyboard layouts. When you add support for a non-US keyboard layout, some of the apps are also installed in a version for that language. Subsequently, Microsoft released an update only for the US-English version of the app. This breaks apps that are installed with more than one language.
In my case, I had added support for Swedish and Spanish-Spain keyboard layouts. For some reason, the Mail app got installed in a Swedish and Spanish version as well. (Which is odd, because I would not actually want the app itself to be in Spanish just because I use a Spanish keyboard layout.)
The latest update to the Mail app only seemed to include support for Spanish-Mexico but not Spanish-Spain, so as a result the app crashed on launch and could not be uninstalled.
My steps to fix it were like this:
1) Try to install the app that has the problem from the Windows Store. When this fails, a fresh error log is added to the Windows Event Log.
2) Open the Event Viewer app check the nature of the problem.
3) In Event Viewer, drill down to log called Application and Services \ Microsoft \ Windows \ AppXDeployment-Server \ Microsoft-Windows-AppXDeployment-Server/Operational.
4) In my case, I would see errors such as this:
Deployment Register operation with target volume C: on Package microsoft.windowscommunicationsapps_2015.6868.41141.0_neutral_~_8wekyb3d8bbwe from: (AppxBundleManifest.xml) failed with error 0x80073CF6. See http://go.microsoft.com/fwlink/?LinkId=235160 for help diagnosing app deployment issues.
error 0x80070003: Cannot register the microsoft.windowscommunicationsapps_17.6868.40731.0_neutral_es-es_8wekyb3d8bbwe package because the following error was encountered while trying to read the package: The system cannot find the path specified.
5) Note the "es-es" part above. This means that it failed to find the Spanish-Spain version of the app XML file when trying to uninstall the old version of the app. If you don't see something like this (adjusted for your keyboard language), then your problem is different from mine, and I can't offer a solution.
6) The next thing to do is to ensure that you can access the C:\ProgramData\Microsoft\Windows\AppRepository folder. This is a hidden folder and the owner is set to TrustedInstaller. You need to change the owner to Administrators and give Administrator full access to the folder, in order to proceed to the next step of the fix. To change ownership, use File Explorer to right-click on the folder, choose Properties and go to the Security tab.
7) I then open an Administrator command prompt and go the C:\ProgramData\Microsoft\Windows\AppRepository folder.
8) In my case, I saw that the app already had a Spanish-Mexico version of the app XML file, but was missing the Spanish-Spain XML file. So, I simply copied the Mexico version to the Spain version, like this:
copy microsoft.windowscommunicationsapps_17.6868.40731.0_neutral_es-mx_8wekyb3d8bbwe.xml microsoft.windowscommunicationsapps_17.6868.40731.0_neutral_es-es_8wekyb3d8bbwe.xml
I got the destination file name from the error message in the Event Log, in step #4. Note that the error message did not include the ".xml" file extension, which is required.
9) I then repeat step #1. In my case, the app still failed to install, but this time the problem was that the Swedish XML file was missing. I then repeated all the steps again, copying the Spanish-Mexico XML file to the path for the Swedish XML file. After this, the problem was fixed and I could successfully install the app from Windows Store.