SQL Server Express support for TLS1.2
You don't strictly need a newer version of SQL Server; however as a general thing I always prefer to be using the most recent version (especially in this case, because in SQL Server 2016 SP1, you get all kinds of new features in Express Edition).

You do need to apply one of the following updates, though (I go through more details in this blog post). They are listed in my order of preference:


Service Pack 2 (+ SP2 CU#3, ideally)
Service Pack 1 + SP1 GDR (minimum) (+ SP1 CU#10, ideally) 
RTM CU#14
RTM GDR update - technically this is all that should be required, but you are missing out on so many other fixes from over two years of updates, this is "the absolute, I don't recommend it, bare minimum" IMHO


That's the gist of it; if you want to get into all the nitty gritty, here is a KB article I'm stealing from Max's deleted post.