Raster has a "none" CRS

My specifications :

• Python 3.9.1
• gdal 3.1.4
• rasterio 1.1.8
• Windows 10 Business
• conda version 4.9.2

I have a raster that has no crs :

os.chdir(path)
file_list= os.listdir()
file_list[0]
>>> RGEALTI_FXX_0605_6670_MNT_LAMB93_IGN69.asc

with rasterio.open(liste_fichiers[0]) as src:
    print(src.profile)
    print(src.crs)
    print(src.bounds)
    print(src.indexes)
>>> {'driver': 'AAIGrid', 'dtype': 'float32', 'nodata': -99999.0, 'width': 1000, 'height': 1000, 'count': 1, 'crs': None, 'transform': Affine(5.0, 0.0, 604997.5,
       0.0, -5.0, 6670002.5), 'tiled': False}
None
BoundingBox(left=604997.5, bottom=6665002.5, right=609997.5, top=6670002.5)
(1,)

For your information, I do have a GDAL_DATA environment variable. (I found this information here).

When I open the raster with QGIS, I can in fact notice that there is no CRS, but on the other hand I can easily select one.
I am looking forward to do the same with rasterio. Here is the code I tried to do so :

with rasterio.open(liste_fichiers[0], mode='r+') as src:
    print(src.profile)
    src.crs = rasterio.crs.CRS.from_epsg(2154)
>>> {'driver': 'AAIGrid', 'dtype': 'float32', 'nodata': -99999.0, 'width': 1000, 'height': 1000, 'count': 1, 'crs': None, 'transform': Affine(5.0, 0.0, 604997.5,
       0.0, -5.0, 6670002.5), 'tiled': False}

---------------------------------------------------------------------------
CPLE_AppDefinedError                      Traceback (most recent call last)
<ipython-input-191-a0546e13d796> in <module>
      1 with rasterio.open(liste_fichiers[0], mode='r+') as src:
      2     print(src.profile)
----> 3     src.crs = rasterio.crs.CRS.from_epsg(2154)

rasterio_base.pyx in rasterio._base.DatasetBase.__exit__()

rasterio_base.pyx in rasterio._base.DatasetBase.close()

rasterio_io.pyx in rasterio._io.BufferedDatasetWriterBase.stop()

rasterio_io.pyx in rasterio._io._delete_dataset_if_exists()

rasterio_err.pyx in rasterio._err.exc_wrap_int()

CPLE_AppDefinedError: Deleting RGEALTI_FXX_0605_6670_MNT_LAMB93_IGN69.asc failed: Permission denied

import rasterio

dst_crs = 'EPSG:2154'

with rasterio.open('without_crs.asc', 'r') as src:
    raster = src.read()
    kwargs = src.meta.copy()
    kwargs.update({
        'crs': dst_crs
    })

with rasterio.open('assigned_crs.asc', 'w', **kwargs) as dst:
    dst.write(raster)