With the plugins provided by bilgekaan, you can indeed display the html file, but still, it has to be converted to C3 and it is just a display without actual interaction.
The best would be for Twine to actually export to XML or a markup language like that.
This way, you could then, in Construct, implement you own way of displaying the story, and could have planned interactions with the use of dedicated XML tags.
You can check this tutorial for how to use XML with Construct.
As for making Twine export to XML, I guess this is a complete feature to add/ask to the maintainers of the project.