The problem of .xls file not getting opened after upgrading to Excel 2016 / Windows 10 is a common problem. This problem may occur after any windows / MS Office update as well.
1. Start the Excel and CTRL+O (or File > Open) > Locate the file and open the file. This should open the file but this may not solve the problem of double clicking the file and opening it.
2.A quick repair usually fixes the file association
3. If this doesn't fix the association, when you right click on .xls file > Open With > You should get the list of programs which can open this file and you should select Excel.
In case, the list of program doesn't have Excel, then choose BROWSE and select Excel.exe. But, in case the folder which you get after clicking BROWSE doesn't have Excel.exe, you will need to find the location of Excel.exe to select Excel.exe. To find the path, you can refer to below link -
4. If there is a file block issue
4.1 Right Click on the file > Properties > In the General tab, you will get Unblock option down below > Check the unblock box
4.2 If you don't get unblock option, ALT+T+O (or File > Options) > Trust Center > Trust Center Settings > File Block Settings > Uncheck the box in front of .xls file