TL;DR
- Know the season
- Know when and where hunting is allowed
- Know the time hunters are most active
- Make some noise
- Most important: wear the right colours
Answer
Good question! Staying safe from hunters is rather the same thing in every country and doesn't apply to hiking or bird-watching only. However, I've added France related information whenever possible.
Basically the answer is mostly: inform yourself before going into the outdoors. You may contact this office for every information you need:
Office National de la Chasse et de la Faune Sauvage
At: 85 bis avenue de Wagram, BP 236, 75822 Paris Cedex 17
Tel: 01 44 15 17 17 Fax: 01 47 63 79 13
Website (in French)
But let's get it a little bit more detailed:

1. Know the season
To get the running seasons and other appropriated dates you've to contact the préfecture because the seasons are managed at a regional level.
The white-tail season is the most dangerous one for hikers and so on since the most hunts are going on. So check especially these dates!
Hunting Seasons
Seasons are managed at a regional level to complement the ecological
needs of the area and its animal and bird life: the dates of the
opening and closing of hunting seasons depend on the département and
the animal species.
While the season generally opens in September and runs until the end
of February the opening is decided by the regional préfet (contact the
local préfecture for dates).
From Angloinfo

2. Know when and where hunting is allowed
It's possible to avoid hunters altogether by choosing your hike
wisely. Many parks, including most national park units, forbid
hunting.
The national parks in France are "non hunting" areas but it can also be difficult to just got out there. It's often prohibited to take expanded hikes and so on. Check out this list of the national parks and get in touch with the appropriated administration of each for further information.

3. Know what time hunters are most active
Many factors, such as the lunar calendar, affect peak times of day for
animal activity, and hence hunting. However, as a rule of thumb, these
usually coincide with sunrise and sunset. It's best to avoid being in
hunting areas during those times since you'll be less visible in the
dim light. But if you must be out at those times, use a headlamp or
flashlight and wear reflective material.
4. Make some noise
This section doesn't apply to every outdoor activity. It would be a little bit stupid to be loud as hell if you're fishing or bird-watching, wouldn't it? :) However, if you can do it, make some noise!
Talk with your companions, whistle, do your best Freddie Mercury
impression. And if you hear shooting, the Washington Trails Association
((US)) advises shouting to notify hunters of your presence.

5. Most important: Wear the right colours
Blaze-orange-colored clothing is of course awesome to make you visible in the woods etc. But the most important thing about this topic is that hunters use these for safety reasons themselves and thus are generally really sensible for these kinds of colours!
Also note that this kind of clothing is also available for your dog!



Wearing a blaze-orange-colored vest, hat, or pack cover is one of the
most important things you can do to stay visible to hunters. It's what
hunters themselves wear for safety. If you don't have any of these
(although you should if you're doing fall/winter hiking) make sure you
wear bright colors and steer clear of earth tones. Avoid wearing
white, though, because it resembles the rear of a white-tailed deer.
The Appalachian Trail Conservancy ((US)) also advises not wearing red or blue
during turkey season.
Subjective conclusion
I also wanted to add my personal subjective opinion. We often think that hunters are kind of trigger-happy. However, they mostly know that they have a great (!) responsibility and normally only shoot if they are sure that they can provide the highest possible safety.
Read more about this topic in the "Principals of ethical hunting":
Respect the opinions of non-hunters
People who are unfamiliar with hunting practices may be intimidated by
the presence of firearms, so be sympathetic to their concerns and, as
much as possible, keep firearms out of sight.
Be considerate, be courteous and show the public that deer hunters are
responsible and ethical recreationalists. Good hunting behaviour will
reflect on people's opinions of all hunters. Rude, illegal and
irresponsible actions can prejudice the community against all hunters.
(...)
Be aware of personal safety
Many hunters today wear camouflaged clothes, which makes them
difficult to see. While concentrating on the hunt, there is a
possibility that you could become lost or be mistaken for game by
another hunter.
To ensure your safety and the safety of other hunters in the field, it
is recommended that all deer hunters wear some form of bright coloured
clothing or hat when hunting. Overseas studies have shown that deer
cannot see colours such as blaze orange and the wearing of these
colours will not affect your hunting success. Many hunters have taken
deer in Victoria while wearing blaze orange clothing.
The wearing of some form of bright coloured clothing is also
recommended when you are carrying a carcass out of the bush. This will
ensure that other hunters do not mistake you for a deer.
"Go afield with a good attitude, with respect for the wildlife you hunt and for the forest and fields in which you walk. Immerse yourself in the outdoor experience. It will cleanse your soul and make you a better person."
By Fred Bear
