How to overlap a geopandas dataframe with basemap?

I have a shapefile that I read as a geopandas dataframe

import geopandas as gpd
gdf = gpd.read_file('myfile.shp')
gdf.plot()

where gdf.crs

<Projected CRS: ESRI:54009>
Name: World_Mollweide
Axis Info [cartesian]:
- E[east]: Easting (metre)
- N[north]: Northing (metre)
Area of Use:
- name: World.
- bounds: (-180.0, -90.0, 180.0, 90.0)
Coordinate Operation:
- name: World_Mollweide
- method: Mollweide
Datum: World Geodetic System 1984
- Ellipsoid: WGS 84
- Prime Meridian: Greenwich

and gdf.total_bounds

array([-17561329.90352868,  -6732161.66088735,  17840887.22672861,
         8750122.26961274])

I would like to use basemap to plot the lat/lon grid on top of it. This is what I am doing

from mpl_toolkits.basemap import Basemap
# Create a Basemap instance with the same projection as the GeoDataFrame
map = Basemap(projection='moll', lon_0=-0, lat_0=-0, resolution='c')


# Create a figure and axis
fig, ax = plt.subplots(figsize=(10, 6))
# Plot the basemap
map.drawcoastlines()
map.drawcountries()
map.drawparallels(range(-90, 91, 30), labels=[1,0,0,0], fontsize=10)
map.drawmeridians(range(-180, 181, 60), labels=[0,0,0,1], fontsize=10)
# Plot the GeoDataFrame on top of the basemap
gdf.plot(ax=ax, color='red', markersize=5)

but this is what I get

That's because the Mollweide projection's parameters (i.e, the proj-string) used by the Basemap are different from the ones of your GeoDataFrame (that is ESRI:54009) :

>>> gdf.crs.srs
'esri:54009'

>>> map.srs
'+proj=moll +R=6370997.0 +units=m +lat_0=0.0 +lon_0=0.0 +x_0=18019900...'

A simple fix would be to call to_crs (with the basemap's srs) before making the plot :

gdf.plot(ax=ax, color='red', markersize=5)

gdf.to_crs(map.srs).plot(ax=ax, color='red')

SN: Using map as a variable name isn't recommended since it's a built-in.