The nation has suffered an unexpected and tragic series of events in the night of Friday/Saturday 13/14 November.
At present many people are in shock, and the media are very present on the scene and making global comments from the safety of their homelands.
It would be reasonable to assume that border controls on Schengen countries around France will be reintroduced which means that all those crossing them will be required to present valid and acceptable identity documentation - National ID cards and passports for the most part - and there will be significantly longer waiting times to go through the borders as each vehicle's or foot passenger's documentation is inspected.
The country has been under the Vigipirate legal status for some time now, and the present incident will result in a more visible police presence, reinforced by the military (often commonly seen at my local airports). French police have always had the right to stop and question individuals, so it would be advisable to adhere to French law to be carrying personal ID when 'out and about'. A photo driving licence bearing your signature and address might be helpful as a minimum. Keep your personal ID documents safe though.
Please respect those who are grieving and who are shocked. Understand that inconvenience at border points is for your security and for those around you and be patient.
Do not change the way you live because of the actions of a minority. Be sensible, sensitive and use your common sense.