<p>Winning the Green Card lottery is a long shot but it is possible. I discussed some of the same concerns you have with an immigration lawyer because I was lucky to with the 2008 DV-lottery.</p>
<p>Signing up for the GC lottery will not affect your F-1 status/application (winning might, but more about that later). When you win the lottery you will receive a notification along with a few other documents you have to fill out and return to Kentucky. Among other things you will be asked to decide between consular processing abroad and adjustment of status in the US. If you are currently in the States at the time of notification, you can pick adjustment of status and you will not have to leave the country for your visa application. If you are not in the States at that point in time, you have to chose consular processing abroad and then return to your home country for the interview, even if you move to the States in the meantime.</p>
<p>Consular processing has its advantages even if you are in the States at that point in time. For example, consular processing in your own country requires only the original version of some official documents (birth certificate, police records, high school diploma...) along with photocopies, while for adjustment of status you need those same documents along with certified translations if they are not in English. Secondly, I am not quite sure how long it takes to adjust status. I chose consular processing, and I just needed to leave the States for two weeks (to do the interview abroad) and now I can re-enter the States as a permanent resident.</p>
<p>Back to possible complications with your F-1 visa: applying for and winning the lottery will not affect your F-1 status. However if you win the lottery before you have applied for your F-1 visa, you have to pick consular processing at which point in time the consulate in your home country will be informed about your "petition for immigration". If you apply for a F-1 visa afterwards, you might be denied a visa because you clearly demonstrated an intent to immigrate.</p>
<p>About your other questions:</p>
<p>You are allowed to remain in the country for 60 days after graduation ("grace period"), and another 12 months if you have your full time of OPT (optional practical training) left. </p>
<p>Getting a H-1B working visa is not quite that easy if you want to work straight out of college with a Bachelor's degree. The reason is that you need to have a Bachelor's degree by the time an employer petitions for your visa. However, that happens in early April before you graduate (at least right now because there is a shortage of H-1Bs) so you cannot apply for a H-1B in the year you graduate. One might think that you could gap that year with your 12 months of OPT and then apply for a H-1B the next year. The problem is that the H-1B wouldn't be valid until October, so you have a period of at least two months (if you max out your grace period) in which you are not allowed to work legally. How many employers would be fine with that? Possible ways around this are going to grad school first or arranging to graduate at the end of the fall semester instead of the end of the spring semester like most other students.</p>
<p>If you marry an American citizen AND you intend live in the States, you can apply for a GC (technically you could also apply for a GC if you did not intend to live in the States, but you would lose it again pretty quickly). Of course you only get it after an extensive background check, and it would be conditional for the first two years (meaning if you divorce early you will lose your GC). At first you would only get a GC and NOT an American passport. However, you can start the naturalization process after having your GC and continuously living in the States for three years (you are only allowed a certain number of months abroad). Whether or not you can keep your French citizenship depends on the laws of France (the US is fine with dual citizenships). I assume that laws in France also state that your wife would only get a French passport if you actually lived in France, so it is unlikely that you and your wife would both acquire each other's citizenships.</p>
<p>Another thing about getting married: I would advise against getting married in the States on your F-1 visa because the adjustment of status procedure takes a while (I have heard stories of upwards one year). The alternative is to apply for a K-1 visa; it is a special visa category for people who intend to marry an American citizen and take up indefinite residence in the States afterwards. After you get your K-1 visa you have to marry within 90 days. The advantage is that the adjustment of status procedure will be a lot faster and you can even get an employment authorization before the marriage takes place.</p>
<p>Edit: Disclaimer - I am not an immigration lawyer and I cannot guarantee for the correctness of anything I have stated.</p>