It seems anyone involved in this in France are opposed to this except Macron. Although he has authority over them I'm not confident it will be moved there in the end.
Macron has pushed for it (to announce as part of his state visit to the UK), the director of the Bayeux Museum has accepted (he is a civil servant, and more subject to politics).
Experts agree that any move is likely to worsen tears in the cloth (a superposition of linen): https://www.latribunedelart.com/bayeux-tapestry-let-s-listen...
The museum where it is exposed is supposed to go through renovation, and experts are worried even to move the tapestry within the same museum just for renovation purposes... one can understand their fears when it's about packing and transporting to the other side of the channel (notwithstanding the amazing level of the British Museum conservation team, among the best in the world).
It is 3"rd page news, 3 days late, and the orange one stole all there fire.