After struggling a little bit, I found a way.

For each page of the file, it was necessary to define into tabula's read_pdf function the area of the table and the limits of the columns.

Here is the working code:

import pypdf
from tabula import read_pdf

# Get the number of pages in the file
pdf_reader = pypdf.PdfReader(pdf_file)
n_pages = len(pdf_reader.pages)

# For each page the table can be read with the following code
table_pdf = read_pdf(
    pdf_file,
    guess=False,
    pages=1,
    stream=True,
    encoding="utf-8",
    area=(96, 24, 558, 750),
    columns=(24, 127, 220, 274, 298, 325, 343, 364, 459, 545, 591, 748),
)

check out this thread

https://www.reddit.com/r/learnpython/comments/7x9inm/project_help_pdf_extraction_to_csv/du7jyzf/?context=3

Martin Thoma's answer is exactly what I needed (PyMuPDF). Diblo Dk's answer is an interesting workaround as well (PyPDF2).

I am citing exactly Martin Thoma's code :

from typing import Dict

import fitz  # pip install pymupdf


def get_bookmarks(filepath: str) -> Dict[int, str]:
    # WARNING! One page can have multiple bookmarks!
    bookmarks = {}
    with fitz.open(filepath) as doc:
        toc = doc.getToC()  # [[lvl, title, page, …], …]
        for level, title, page in toc:
            bookmarks[page] = title
    return bookmarks


print(get_bookmarks("my.pdf"))

The answer depends if the question is general or specific to a single form. Your approach is reasonable for the general case, but there will be variability. If you have a pdf form that is a single form or report that has been created with different data at each iteration consider converting the form from pdf to postscript then see if you can parse the postscript.

Two utilities do this: pdf2ps and pdftops Try each. This approach may benefit if you know some postscript. With some luck the needed fields may be simple text strings. Worth a try.