It is pretty tough to "not" be anxious about these things just try to relax. When I staged in France at a Michelin one star I cut my finger badly the first day. I was grateful to God that he caused me to laugh about it and not take it so seriously. At the end of the day simply do your best and walk out of there knowing you did your best. I would like to give you some advice though. What is your experience level? If you are still learning your way around the kitchen this may not be the best fit for you. Here is what I am trying to say.
If you are still just learning the basics (learned them within the last year or so) then you simply won't get everything you can out of this experience. You see you are still at a stage where your learning the basics and when you go to a 3 star place you will only be focusing on basics. The more experience you have under your belt the more you will get out of a high end restaurant like that. Many of my fellow class mates opted for 3 star restaurants for the externship and they ended up cleaning lettuce and cutting herbs because that was the extent of their experience. Pay attention to what they have you doing and if you are only cleaning peas, lettuce etc etc after 4 weeks move on. You don't need to be in a 3 star to learn those things.
When you are working with a shorter stay like a stage you want to maximize your learning. So when you go to a 3 star like this you should be focusing on techniques they are using and know enough to simply observe, take a few notes and be able to replicate as well as ask intelligent questions. If all you know are stocks, chopping, mincing then you will probably not get as much out of it because you simply don't have the experience yet to know what to look for. My advice would be go for a few weeks but pay attention to whether you are really learning anything. I was very glad I took the advice of several chef colleagues who cautioned me about going to a Michelin 3 star in France. I went to a one star and had a fantastic experience. I actually got to cook handle fish learn techniques etc.
Thank you so much for you advice. I have a one day stage with them and my externship would be until the end of this year. The same time I would graduate from school. I'll take what you've said and decide once my term is done if this is for me. My goal is to document is much as I can and look to see if it is benefitting me.
Go into the stage with respect and humility. Whatever level of experience you have, show great respect for everyone you meet, pay attention to what you are told and when corrected, keep your mouth shut and follow orders.
You can relax a bit by doing as Nicko suggested and simply doing your best. You will not be allowed to do anything they don't feel you are ready for. So you will start out with simple tasks and move on to more challenging tasks as they see fit.
What to look for.
Throughout your stage, however long it may last, watch carefully how the kitchen operates. Note the total number of people in the kitchen, note what their tasks are, how the work area is set up, everyone from dishes to expeditor.
How do they communicate with each other, how is instruction given.
If you happen to see a delivery, note the amounts of things, what kind of product it is. How often is the delivery. Is there any negotiation between the purveyor and the chef? Does the chef check the order for quality, inspect the items, return or refuse anything? Why did he/she return or refuse the item?
Note the behavior of the cooks. How neat they are, how focused they are. How do they interact with each other?
Note the behavior of the staff before, during and after service.
Note the interaction between cooks and waitstaff before, during and after service. How do they communicate? About what?
Get a copy of the menu. Note the number of items on it. See how the items are divided up among the cooks for production. How many menu items are the responsibility of each station?
Note when prep is done. How much prep for each item? Are the recipes complicated or simple? What gets labeled and in what way is it labeled?
How noisy is the kitchen? What is making the most noise? Is everyone talking? About what?
If you see something you don't recognize, when you have an opportunity to do so, ask what it is.
What tools, in addition to knives, are being used and for what? How does each menu item get plated? Is it a simple or complicated plating? How may cooks does each plating require?
Note simple techniques. Note the quality of each ingredient. How does the ingredient change from delivery to plate?
How is the walk in and other storage areas organized?
Are the cooks cleaning as they work? In what manner do they do that?
Were there any special customer requests? how did the kitchen handle them?
As Nicko noted, you may not learn advanced techniques, but you can learn much about everything else. Overall, while you are performing simple tasks, your eyes and ears should be wide open, taking in everything around you. Not all three star Michelin places are the same as each other, but they are all operating at a very high level. When your stage is over, you should have a clear picture of how such a place operates and use that knowledge to inform how your place will operate some day and a clear idea of how to conduct yourself from here on out.
Dear Sir, while only a home chef, I really appreciated your insights on the things to look for when observing the operations of a top kitchen staff. I am the president of our local cooking club and plan to share your thoughts with our group. I love to ask to see professional kitchens in operation and have done so across the US, Canada and France. I always learn something new.
Thank you again for your post.
PS: I would really appreciate it if you would come here and open a fine dining restaurant. One more greasy burger, or deep fried shrimp may send me around the bend!