Note: If your blog or website got content which links to third party sites with and without HTTPS has no impact on this.
Caution: Take backup of your files and databases before you proceed with this.
How to Fix WordPress?
Before you dive into this, ensure you got proper 301 redirect to your final version of your URL. Example: https://example.com or https://www.example.com
To fix this issue, you just need to find and replace your old URL start to new URL start.
Example: If your site was like: http://www.example.com/blog and you changed to https://www.example.com/blog then just find http://www.example.com and replace with https://www.example.com.
Note that you are replacing only part of your URL, so if you find with a slash then replace with a slash and vice versa.
Just download Interconnect database search and replace, place it in your WordPress folder and load the script in the browser, do a dry and then live run.
Download your copy of entire database, open it in a text editor and just find and replace as mentioned above. And then woerwrite your database.
It should work.
How to Fix static or custom websites?
Just download entire files from the server, replace all http with https except the link you might be pointing out to a third party.
Hope this will help.