You don't need Fiona to write a GeoJSON file

    features = [feat for feat in Fiona.open("a_shapefile.shp")
    layer = {
         "type": "FeatureCollection",
          "features": features}
    # save json file
    import json #or GeoJSON
     with open('result.geojson', 'w') as outfile:
         json.dump(my_layer,outfile)

No CRS is explicitly defined inside the original GeoJSON format but you can add a crs in my_layer. The coordinate reference system must be in a special format (OGC CRS URN, see [What's up with the GeoJSON spec and CRS as a IRM?][1]) not compatible with the Fiona .crs (PROJ4 format)


      layer = {
         "type": "FeatureCollection",
          "crs": { "type": "name", "properties": { "name": "urn:ogc:def:crs:EPSG::31370" } },
           "features": features}

Or you can use [PyGeoJ][2]

    import PygeoJ
    newfile= pygeoj.new()
    for feat in fiona.open('a_shapefile.shp"):
         newfile.add_feature(feat) 
    # now you can add many parameters 
    newfile.add_all_bboxes()
    newfile.add_unique_id()
    newfile.define_crs(type="link", link="http://spatialreference.org/ref/epsg/31370/esriwkt/", link_type="esriwkt")
    newfile.save("test.geojson")


  [1]: http://gis.stackexchange.com/questions/15953/whats-up-with-the-geojson-spec-and-crs-as-a-irm
  [2]: https://github.com/karimbahgat/PyGeoj