The short answer: it depends on the length of your (the J-1’s) stay. If that is not longer than 30 days, you should not have any problem with the J-2 remaining in the country (see @Dorothy’s answer).

If your stay is (intended to be) longer than 30 days, the J-2 cannot stay (see @Dorothy’s answer), but one question is whether the J-2 can at least stay for the first 30 days of your longer-than-30-days absence. Considering that you usually have to complete a notice of absence, an out of country request or anything similar for stays longer than 30 days, I understand from the wording of the out of country request at University of Washington that the J-2 has to leave at the same time as the J-1:

We certify that:

• […]
• J-2 dependents will depart the U.S. with the J-1 Exchange Visitor

Regarding your specific options:

I go to France alone for a couple of weeks, go back, and then we go to France together for three months.

This should be fine, as long as a couple of weeks is not longer than 30 days.

I go to France alone; my wife joins me there a month later; we return together three months later.

This will be a problem if your three-months stay is intended to be that long from its beginning. The J-2 has to leave with you, if my reasoning above is correct.

I go to France alone; my wife joins me there a month later. While there, I learn that I get a job. I resign from my U.S. position, cancel my visa and neither of us returns to the U.S. in the fall.

From an immigration point of view, this is no different from the previous option. The J-2 has to leave with you, and no one will care whether you ever come back or not. I see no problem with resigning from your position; however, I generally wonder whether a non-completed J-1 program might jeopardize future J-1 applications. You might need to figure that out with your sponsor, but it should not make any different whether you do this while in the US or not.

The one open question is what happens if you leave for an intended period of time not exceeding 30 days, and don’t return as planned. It would not be credible for me to speculate what exactly happens, but I guess there can be no doubt that you need to inform your sponsor (compare the notice of absence: “I will inform ISSS and my department if my schedule changes.”), and that the J-2 needs to leave as soon as your sponsor determines that your stays exceeds 30 days. I do not know whether that counts as overstaying on her part; nor whether that impacts your ability to return into the program if you fail to find a job in France.

Note that you are planning to “spend a few months in [your] home country for job interviews and vacation (while keeping [your] legal J-1 status)”. This would involve convincing your sponsor that your absence is program-related (compare, again, this notice of absence). If you fail to do that, there is a possibility that they terminate your J-1 program, which means that you and the J-2 have to leave, maybe immediately, but certainly without a 30-day grace period (which you only get when you complete the program).

Disclaimers

• This is not legal advice, obviously.

• Adding to @Dorothy’s answer, I have found this on the webpage of University of Minnesota:

Please Note: It is unclear how the status of a dependent visa holder is affected if the dependent remains in the U.S. when the principal visa holder is temporarily absent from the U.S. It is recommended that the J-2 not remain in the U.S., if the J-1 will be absent for more than 30 days.

So even people having educated opinions (such as those at that particular International Office) may not know the exact answer.

I realize this is not your program, but it is a US Federal Agency applying the J-1 visa regulations, and the explanations respond to your concerns:

Travel Outside the United States

J-1 visa holders and their J-2 dependents can travel independently of one another. However, a J-1 visa holder cannot leave J-2 dependents alone in the USA for more than 30 days. Doing so will result in both the J-1 principal and J-2 dependents being “out of status” and possible program termination. Exchange Visitors should consult with an IVP Program Specialist in the International Programs Office when requesting travel validation on their DS-2019 forms to make certain traveling outside the US without their dependents will not jeopardize their program status.

If the J-1/J-2 visa holder goes home for a vacation, contact the US Embassy/Consulate to request information on the process of acquiring a new stamp/visa in the new passport.

Dependents (J-2 Status)

The J-2 dependents are not required to travel and enter the US with the J-1 principal, but may follow at a later date. J-2 dependents must adhere to the same regulations regarding departure dates and grace periods as the J-1 principal. Also, should the J-1 principal be out of the US for more than 30 days at a time during the course of the program, the J-2 dependents cannot remain in the US without the J-1 principal.

Although family members usually enter as J-2 dependents, they are not required to do so. They may enter as tourists (B-2) or on another visa type if they qualify.