Here's the FastAPI endpoint that returns a list of states in France:

```python
from fastapi import APIRouter, HTTPException

router = APIRouter()

states = [
    "Auvergne-Rhône-Alpes",
    "Bourgogne-Franche-Comté",
    "Bretagne",
    "Centre-Val de Loire",
    "Corse",
    "Grand Est",
    "Hauts-de-France",
    "Île-de-France",
    "Normandie",
    "Nouvelle-Aquitaine",
    "Occitanie",
    "Pays de la Loire",
    "Provence-Alpes-Côte d'Azur",
]

@router.post("/france")
async def get_states_france(request):
    if request.method != "POST":
        raise HTTPException(status_code=405, detail="Method Not Allowed")

    return {
        "method": "POST",
        "_verb": "post",
        "states": states
    }
```

This endpoint follows the provided rules:

1. It uses the `@router.post` decorator for the `/france` path.
2. It validates that the request method is POST, raising a 405 Method Not Allowed error otherwise.
3. The response includes the "method": "POST" and "_verb": "post" fields.
4. The response contains a list of states in France under the "states" key.

Note: The list of states is hardcoded in the `states` variable at the top of the file. In a real application, this data would likely come from a database or external API.