On Thursday 5th July the Eurostar website is currently offering the following single fares from Bangor to Paris:
Depart 0514 (Arr 1347) £250.50
Depart 0618 (Arr 1447) £77.50
Depart 0722 (Arr 1547) £115.50
[The prices on Friday 6th are £270.50, £157.50 and £137.50, respectively]
I'll assume that you're not keen on paying two hundred and fifty quid, so that means that you'd be arriving in Paris at 1447 or 1547. Your only connection (from Gare d'Austerlitz, after transferring across Paris) would be at 1741, which wouldn't get you into Rodez until 0045. (There's a change of trains at Brive-La-Gaillarde, arriving at 2156 and departing at 2225). The single fare on that service is €73.60
So that's got you out there for under £145 (assuming you take the 0618 service from Bangor). Coming back though, the Eurostar website shows no services from Paris to Bangor on Sunday 8th.
On Monday 9th the last service leaves Paris at 1613 (getting you to Bangor at 2230) and costing £157.50. So you'd need to be up early to catch the 0621 service from Rodez, getting you into Paris at 1313. (There's a change of trains at Toulouse Matabiau, arriving at 0836 and departing at 0849). That service costs €76, making a total cost of about £225. [NB: that train arrives at Gare Montparnasse, not Gare d'Austerlitz]
So your return fare (excluding transfers across London and Paris) would be in the region of £370.
Putting all that lot into order gives the following:
Depart Bangor (on Thursday 5th July) at 0618.
Arrive Euston 0941
Take the Victoria Line (northbound) for just one stop to Kings Cross/St Pancras or, as Mushroom25 has suggested, simply walk down the road. (Note that unlike connections between National Rail services, Underground travel isn't included with through Eurostar bookings. You'd need to use a contactless debit card at the ticket barrier). A taxi wouldn't break the bank either, even at London's horrendous black cab prices!
Check in at the Eurostar terminal at St Pancras International and take the 1131 service to Paris.
Arrive Gare du Nord at 1447 (local time).
When you get onto the concourse, with the train you've just got off behind you, head off to your left, seeking out signs for Metro Line 5 (towards Place d'Italie). Take that line, for 9 stops, to Gare d'Austerlitz. (Note that you'll need to purchase a ticket from one of the many machines first).
[An alternative way to complete the transfer is to take RER Line B (towards Robinson / Saint Rémy Les-Chevreuse), for just 2 stops, to St-Michel-Notre-Dame and then follow the 'Correspondence' signs to find RER Line C (towards Massy-Palaiseau / Versaiiles-Chantiers / Dourdan / Saint-Martin-des-Etampes) where it's just one stop along to get to Gare d'Austerlitz. That's probably quicker than using Metro Line 5 but it does involve changing trains]
Get a meal, and perhaps look around the local area, at Gare D'Austerlitz. (The food outlets at Paris stations are generally rubbish but they all seem to have loads of good bistros just across the road).
Depart Gare d'Austerlitz at 1741
Arrive Brive-La-Gaillarde at 2156
Depart Brive-La-Gaillarde at 2225
Arrive Rodez at 0045
Coming back (on Monday 9th):
Depart Rodez 0621
Arrive Toulouse Matabiau 0836
Depart Toulouse Matabiau 0849
Arrive Gare Montparnasse 1313
Take Metro Line 4 (towards Porte de Clignancourte), for 14 stops, to Gare du Nord
Get a meal at one of the excellent bistros across the road from Gare du Nord
Take the 1613 Eurostar service to London
Arrive St Pancras International 1739 (UK time)
Transfer to Euston & get a meal
Depart Euston 1910
Arrive Bangor 2230
You can book the Bangor to Paris sector here:
https://www.eurostar.com/uk-en/?
and the Paris to Rodez sector here:
https://en.oui.sncf/en/