How much job flexibility did guilds offer? If I was a member of a guild in one medieval French city and moved to another medieval French city, would I automatically be a member of the same occupational guild there?

I've answered these sorts of questions in the past on building trade guilds. The biggest problem here is that I'm drawing a blank on a good source for this particular answer. Let me try to sketch out a general answer and then hopefully I can locate a good source (sorry mods, I know this should really go the other way!). Note that I'm going to talk strictly about guilds for the building trades (which would include plasterers, carpenters, and masons).

The two key variables in the question are when, precisely, in medieval time we're talking about, and which guilds, specifically, we're talking about. The guilds grew, substantially, in influence, size, and organization as the centuries rolled forward, so it would be typical to find very loosely organized guilds early on, and pretty highly regimented guilds near the end of the period. Also, the guilds for carpenters and masons grew in size and organization much more quickly than plasterers and painters, e.g. One of the key reasons for this is that masons and carpenters served, on smaller and mid-sized projects, as the de facto structural engineers for the project--they designed the load-bearing beams and the structural attachments between those beams and the walls (or, in the case of full masonry walls, where the walls themselves were load-bearing, the attachment from the roof rafters to the walls). Because this implicated safety and stability, regulation of the trade became much more important than those trades and guilds that dealt more with architectural finishes (again, plastering and painting chief among them).

So, those caveats aside, what sort of mobility would you have? First, understand that you'd have no mobility unless/until you were the equivalent of a journeyman: you had completed your apprenticeship and were deemed capable, by your instructing master, of working on your own. Typically, upon graduation from your apprenticeship, you would receive a written letter from your instructing master, indicating that he had trained you and deemed you capable of doing the work. So, if you wanted to move to a different town, the typical process would be to move, find local members of the guild, and present yourself to them, by presenting the letter. What happens next could vary wildly based on time, place, and trade.

You may have moved to a town with no strong or organized guild. So, you show your letter to the local mason, he grunts, shrugs his shoulders and you both move on. If the locals feel particularly protectionist, they might bad-mouth the "newcomer" to the locals--meaning that the guild doesn't always welcome a newcomer with open arms. At the other end of the spectrum, you might move to a town that has a guild hall, where you go and meet the current master of the guild, and he formally accepts you, either based on your letter or by giving you a test (a difficult piece of work to perform to demonstrate you know what you're doing). Upon being accepted, you would be treated as a brother in the guild.

To your question, it certainly wouldn't be "automatic," and only a fool would move and then just hang out a shingle and start doing work. You would need to seek out the local guild members and affirmatively seek their approval/acceptance. I would imagine, but can't remember reading specifically about, some guilds in some cities at some times might be very protectionist and would work hard to keep newcomers out.

If we fast-forward to today, we see all of these traditions carried forward in the current operations for building trade unions. If you are a member (to use an example) of a the electricians union in Toledo, what you actually are is a member of the Local (i.e., the local chapter of that union). If you move, you'll need to join the new Local in your new area. You'll do that by going to the union hall and presenting your training papers and certificates to the Local, so they can credential you into their Local. I.e., having been a union electrician in area X, you're absolutely not automatically a member of the union in area Y.

Let me hunt down a good source or two.

EDIT: SOURCE AHOY! Ogilvie, Sheilagh; Institutions and European Trade: Merchant Guilds, 1000–1800 (2001) at (among other treatments) pp. 51-57. Ogilvie's work is a great one on medieval guilds in general, so it's not surprising that this is covered in some depth.