First, independently between wood and pellets, it depends how sustainably the wood you will use is farmed. Let's assume its farmed the same, so we rule this factor out - and France forest are among the most sustainably farmed I think
Inconvenient of pellets:
(little) amount of energy to drive the feeding mechanism
mechanism can dysfunction
another amount ...
Pellets are sustainable, typically made from poor feed-stock wood products.
The heat produced is also evenly distributed, unlike a woodstove-high when fully loaded and lower as the fire extinguishes itself.
I have been heating with pellets for 10 yrs in a cold climate-New England in the USA.
What you are proposing -- to remove the heat energy from the cooking fumes prior to exhausting them -- is complicated by two factors*:
Heat engine performance is limited by the temperature difference between the source and sink (more info). If you tried to transfer the heat of the cooking fumes to the ambient air in your house, the temperature difference ...