Question: My internship mission consists in recoding an entire software which was coded 8 years ago by a current senior developer of the company in another language.

The only trouble is that I changed the organization of the software from bottom to top. I switched to MVC instead of the "all in a file" pattern for example.

How do I show him my current work without sounding like "your previous work sucked so much, that's why mine is so different" ?

Answer: 
Was this person a senior developer when they write the code 8 years ago?  

Probably not - so the code wasn't 'senior developer quality'. 

Unless they are still writing code the same way they did back then, you should have little concern in showing how you've improved on their work using current best practices.
The first step is stop seeing your work this way: you did not receive the task to rewrite bad code but to port it to a new language.
That's what you did and that's it.
Different choices are to be expected when porting, moreover if the codebase is old, so if nobody goes down that slope you shouldn't worry about someone seeing a judgement in your changes.

As a side note maybe you are not fully aware of all the reasoning behind the choices made 8 years ago that led to that code: maybe that was the best they could do at that time with the tools, constraints, specifications and so on.